Can dirty throttle body cause 02 Camry to be sluggish?

Yes it can but also check air filter and clean throttle body replace fuel filter if have not done so in a while add Lucas Fuel Injector Cleaner to gas tank.

When was the last time you did service in the Trany? I don't think a dirty throttle body will cause Trany to shift with long delay and I thing you are getting stuck in 2 gear on take off. Check your trans fluid and do a service but you should get it diagnose by a shop To get a diagnose