If I set HP for all Unit X's owned by player 1 at anywhere to 1%, Will Unit X's owned by player 1 that are inside of a dropship get their HP set to 1%?

No.
Next time, for a question as simple as this, make your own test map.
I didn't know the answer, and tested this out in literally under a minute.

I believe the answer to that is yes. That is however, unless you constantly set their health to something else. But I'm pretty sure that it is a yes. Test it out. It takes like 2 minutes to makes triggers for it.

EDit: Woops, nevermind i guess lol. But what I said stands with Vrael.