In a word, the answer is no! There are a lot of reasons why.
1. Anyone over age 40 wont be allowed.
2. There are TSA officers that have never handled a firearm.
3. There are too many people in a close space in checkpoint screening.
4. The expense of training and arming them is too high.
5. The liability is too high.
6. There are TSA officers that dont want to be armed.
7. There are TSA officers that would quit if it came down to that.
8. The qualification process would be to hard to implement.
etc