I'm at a location with 4 clues on it, which is the most clues of my revealed location cards.

I play Drawn to the Flame , then draw an Encounter card.

I draw Locked Door, which says attached location with most clues cannot be Investigated.

Do I still earn the 2 clues from playing Drawn to the Flame? I'm thinking the answer is "yes" since I'm using a Mystic ability, not performing an Investigate action.

Care to weigh in?

You're good, Locked Door only prevents you from Investigating as you say (the Investigate action, or any card ability that says "Investigate" in bold like Rite of Seeking). Any other means of getting clues such as Drawn to the Flame will still work.

Welcome to the world of finding ways around restrictions! Here's another way to get around locked door (and isn't tricky): have Roland defeat an enemy at that location.

Or buy them with Intel Report, pay Lola Santiago to pick one up, Eavesdrop on an enemy, Work a Hunch... the list goes on!