I was chosen for one of these programs when I was in grade 4 and got perfect on all the standardized tests, including the bonus questions. Then they gave me the IQ test. I qualified for the "gifted" school. I went there one day...and I was not feeling the atmosphere. Most of them kids was fukking WEIRD...and I decided I'd rather have a regular social life than become an egghead who could only relate to other gifted nerds. So, I told my mother that I wanted to stay in regular school. shyt in grade 2, they wanted me to skip TWO grades...but again, I said "nah bro" as I realized it would not be a good social situation for the kid.
I don't regret my decision.
If your kid is really smart he will be really smart regardless of whether he goes to public school or a special school, as long as you recognize his talents, nurture them, and keep in contact with his teachers and schools so that they know how to nurture him as well. As someone who works closely with the school system, teachers treat children of concerned parents MUCH better than kids whose parents don't make that effort.
Good luck.