I gauge this in a lot of ways. Mostly by popular culture.
Definitely. It's easily the most influential component of American culture. The popular cultural influence includes a long list from the creation of the gospel and jazz to rock and roll, and hip hop. Since America is the leading cultural on the world, AA is too. What becomes cool in America eventually becomes cool everywhere else.
But I think the larger influence is the AA community's effect on America and the concept of struggle, independent spirit, and innovation. This country owes its leadership position in the world due to the fact that it's the best place to come to make your fortune, get educated, invest money, and do all of that with the relative certainty that a government won't arbitrarily change a law and take it all away.
If you honestly look at the countries around the world that are "competing" with the US, you really can't say that someone would be better off parking their money there and growing their wealth for 30 years. Russia? Crime or the government can just take it. China? There are huge parts of their land turning into desert. They've got entire cities that shut down for days at a time because rivers stop flowing. Just breathing outside is like smoking 2 packs a day.
Back to my point. It's no accident that the US ended up in it's position. The independent spirit drives the innovation and the willingness to persevere again and again before succeeding is viewed as a critical factor to being successful. This all certainly has roots in the philosophers and independent thinkers who wrote the Constitution but it has been carried out through all successive generations.
Precisely because AA wasn't allowed to be part of the plan is why their contributions were so influential. They had to fight just to get heard. They had to fight even harder to get their ideas adopted. Even then, many times those ideas and inventions were then stolen. But their significance and influence cannot be denied. Let's look at the list.
George Washington Carver - His list of inventions is way too long to list here. Most influential of all is that he invented the concept of crop rotation. This has led to increased yields, higher nutritional value, and more successful crops all over the globe. The importance and influence of his thinking cannot be overstated. And before any of this he had to get a loan from a bank to go to college. After he got accepted by one college who refused to let him in when he showed up. He then became the first black student ever (later the first black teacher ever) at Iowa State. Then he got his Masters of Science from there. The struggle he had to go through just to allow his ideas to be accepted goes on from there but the point is he was brilliant and had to work three times as hard just to get heard.
George Crum - Not as scientifically important but he invented the potato chip in 1860. That's now sold all over the world.
Granville T. Woods - Invented a telegraph based system to control train traffic in 1887. Think about how important the railroad was to the growth of this country. He made it safer and more profitable.
Elijah McCoy - Esacped slavery through the underground railroad and went to Scotland to become a master mechanic and engineer. In the mid 1800's he invented a device that automated the lubrication process for train axels and bearings. The importance of the device was the trains didn't have to stop. He couldn't get a patent so people stole his idea but when people wanted the best device they asked for the "real McCoy" If the invention of a phrase based on something you created is still used over 100 years later isn't culturally influential, I don't know what is.
Lewis Latimer - If you enjoy being able to see at night, don't thank Thomas Edison, thank Lewis Latimer. He was the one who first used a carbon filament in the bulbs. Edison's bulbs burned out in 15 minutes and it wasn't until Latimer's longer lasting filament was widely employed that the light bulb became a practical purchase. He also invented an early form of air conditioning.
Sarah Breedlove - She worked for 18 years washing people's clothes until she invented a hair care product, started Madame CJ Walker and became America's first female self-made millionaire.
Dr. Charles Richard Drew - Invented the process of separating red blood cells from plasma. That led to the creation of the first blood bank. His set up of blood banks for the US Army and Navy in WWII remains the model for blood banks to this day. He resigned when officials insisted on segregating blood by race. He knew that this was a waste of time and could cost lives. Nevertheless, his invention and blood bank has saved millions of lives.
Philip B. Downing - His safety enclosure design for mailboxes in 1891 let people confidently place letter in the mail without the risk of theft or damage by rain. The impact of this invention in economic terms is absolutely immeasurable.
Garrett Morgan - He was self-taught and never had any formal school beyond 6th grade. But he still invented the gas mask which saved hundreds of thousands of soldiers and firemen. He also invented an early version of the traffic signal because he worried about traffic accidents.
Dr. Patricia Bath - Invented and patented the device used to perform laser cataract surgery in 1988. Her device let people who had been blind for 30 years see again. You can't get more influential than curing blindness.
Mark Dean - Holds three of IBM's original 9 patents for the personal computer. He co-invented the part of the computer that let's us plug in other devices and control them.
The list goes on and on but I stop there to illustrate a point. What these AA men and women accomplished and contributed to the world was done under the worst possible repressive and prejudicial conditions. Yet their contributions to everyday lives in the world is undeniable.
But it is the spirit of overcoming obstacles and persevering against all odds that contributes to the greatness of America. It's the willingness to not take no for an answer. It's proving that whatever your current station in life you have something important to say and something to contribute. It's the stubborn refusal to be put down. Those attributes of these great men and women are even more important to our country.
I've worked with people from all over the world. Other cultures don't foster that kind of independent spirit. People in Europe just don't walk into their manager's office and say "hey I've got a good idea". In America, you can. I'm not saying that everyone has equal access or that it's a fair system for everyone, far from it. But you can contribute important ideas. You have.
AA America is the heart and soul of this country. Even after doing so much to build this country and contributing in such important ways without thanks or credit or compensation, you still persevere. That is a lesson for the world. Head up, chest out and walk with pride. You're part of an incredibly important group of people.