I learnt this the hard way by pressing my second son's claim on the HRE while he was still in a bishopric. Result - the Holy Roman Theocracy (of Doom). I reloaded and revoked his title first and then things went as planned except for his subsequent deposition and somewhat painful death on the battlefield.
Funnily enough, this doesn't seem to work as I'd expect for my latest weird inheritance scheme. I married my female heir to the heir of Denmark, and I was contemplating giving that prince of Denmark, now in my country, a piece of land so they don't get the fertility penalties from being in my overcrowded court (in whose state something is most certainly rotten). However, both of us have High crown authority. I found that if I gave him a Town, turning him into a Mayor, he still inherited Denmark normally as a noble when I assassinated his dad. Which sort of confused me two ways because he, being landed in a foreign country, was able to inherit at all despite the High crown authority, and that he didn't turn Denmark into a Serene Republic.
I'm just guessing from what I've read above, but I gather that this was able to happen because I specifically did not give him a barony title which would establish him in a foreign country and thus exclude him due to High crown authority, and that inheriting the throne of Denmark turned him back into a regular noble, who now happens to own a town.