To answer OP's question, it's certainly possible that Smith loses his job to Chase Daniels. If KC keeps losing games, Andy at some point has to make the change and Chase is next man up. On the other hand, Chase is 29 and hasn't necessarily shown he can start in the NFL till this point. So the chances of him becoming a bonafide starter are slim. Teams don't have much tape on him so even if he does well at first that doesn't portend he'll continue on that trajectory. That said, his scouting report contains more positives than Aaron Murray from Georgia, so maybe he was a better prospect from the outset.
This Rotoviz article makes a case for Daniel' having comparable stats to starters like Big Ben and Luck, however his closest comparisons in terms of Y/A are Kyle Orton and Geno Smith. He can be serviceable:
The World’s First Ever Chase Daniel Fantasy Football Article!
Player Profiler compares Daniel to Kellen Moore, whom could be a starter if not for his unsetting and unfortunate lack of any arm strength:
Chase Daniel - Player Profiler