Yes, going off HRT will make hair try to grow back in places where you want to get rid of it. That's what testosterone does. So you can continue to fight the fight against body hair, but you're fighting at something of a disadvantage if you're not on hrt.
But no, you don't have to stay on testosterone. My insurance now covers GRS and they have a clause whereby patients must be on HRT for a year as a condition of coverage, so it can have some repercussions like that. Similarly you might need HRT as a condition of a doctor's not to change your gender marker on your driver's license, passport, birth certificate, etc. — but once you do that, nobody will be checking that you take your meds.
You should absolutely transition fully, and define fully as whatever it means for you, given your goals and your means and your priorities in life.