No. They isolate for 7–14 days before a launch. I think space shuttle was only seven, but I remember moon launch as fourteen, but I might have that confused with isolating afterwards or confused with some other isolation period.
Influenza incubation is very short, less than 72 hours, so the chance of developing flu would be close to zero.
Actually, now that I think about it, maybe moon launch was fourteen days because we had more diseases with longer incubation still circulating more than when space shuttle was happening. Now, with covid19 maybe they would extend isolation time again. Just wondering out loud.
The astronauts go through thorough health checks and isolation to do everything possible to not carry a contagious disease into space that they would need medical care or get others in the crew sick.