I bet you would. It wouldn't have to be an unsolved problem; one to which they couldn't too-quickly work out the answer would suffice. The sort of problem you'd need would be one for which there's a plausible-seeming argument for each of two conclusions -- e.g., the "Feynman sprinkler" problem -- and then you'd frame the question so as to suggest one or other of the arguments.

But it would be disappointing and surprising if physics professors turned out to do no better at such questions than people with no training in physics.

(If you make the question difficult enough and give them little enough time, that might happen. Maybe the Feynman sprinkler problem with 30 seconds' thinking time would do. Question: How closely analogous is this to the trolley problem for philosophers? Question: If you repeat the study we're describing here but encourage the philosophers to spend several minutes thinking about each question, do the framing effects decrease a lot? More or less than for people who aren't professional philosophers?)

Physicists don't claim to be experts in logical consistency.