Hello, I hope you are doing well

There are certain things which you need to understand about seat allotment and document verification.

Suppose you have been allotted a seat in round 1 and you choose to float your seat for further upgradation, that means you are not satisfied with your current seat and you want a better college/branch. So, the scenario which you said about getting a seat then verifying documents and hoping for a better seat in round 2 can't happen together.

Document verification  generally takes place after freezing of seat or at the end of all rounds, so if you aren't satisfied with your current seat you can keep your seat on float otherwise freeze it.

Hope this helps