Can I upgrade to Unity pro during game development?

Leave plenty of extra time to fix weird upgrade bugs.

It will probably take 5 minutes and work perfectly. But there's those 1% of crazy cases where you messed up, it looked fine in Free so you didn't notice, but Pro is now hating it.

That's usually the rule for all upgrades -- you are entering the unknown, so be ready.

There's not actually any upgrade. Pro is just a license, not a different app or anything.

That's kind of my point. Things that barely even count as a change, so "can't possibly cause problems," are what get people in trouble.