The obvious problem is that there's no judgment of "correct" or "incorrect". Analogizing to a bitcoin proof-of-work, it would be as if a hash beginning with more zeroes always outranked a hash beginning with fewer zeroes, but there was no way to know whether your hash started with "enough" zeroes or not.
I'm going to guess that if you inspect each project it has a purported (positive) medical use and you'd have to make a judgement call on each project based on good knowledge of biology as to whether it had a bioweapons application.
I doubt, but cannot say for certain that F@H won't have any projects that are stated as bioweapons and I'm skeptical that somebody working on a bioweapon would try to cloak its intent, and come up with a plausible medical application so they could get free F@H cycles.
I remember the days of logging into national labs supercomputers and seeing the other jobs on the system, such as job_name "submarine_geometry_optimizer" and the user_name was "electric_boat" or something similar.
Proof-of-work works because a theoretical attacker would have to invest huge resources into an attack. For bitcoin it's trivial to say "for attack scenario X an attack has to spend at least Y", and as long as the expected reward is lower than Y the network is safe (that's for example one factor you use to determine how many confirmations you wait before accepting a payment). If the attacker could conceivably gain money outside the cryptocurrency for performing the proof-of-work, that makes the whole calculation less predictable, and likely exposes you to more situations where an attack is actually profitable.
Protein folding, where the value is speculative, cumulative, and difficult to cash out, is an excellent candidate. Especially since the ability to realize the value of a given fold is diminished by openly publishing it, which is a requirement of proof of work; the folding computation thus becomes a positive externality of the cryptocurrency, since everyone can use that knowledge as an economic stimulus.
I'd like to see someone try it.