Yes, assuming that the challenge hasn't had significant work on it already
The truly difficult tasks can be very interesting to work on, and you won't know whether they're impossible unless you post them. If it turns out to be impossible, or nobody answers, no real harm is done. If it turns out to be possible, we have a very impressive solution, and everyone benefits. So the potential downsides are small, and the potential upsides are large. (The best example of this happening in the past is probably this question; when it was posted, there was doubt as to whether it was possible, but it turned out that it was, and apparently 442 users (at the time of writing) were interested to see the result.)
On the other hand, the challenges should be ones where it's reasonable to consider that someone would actually work on the problem because of PPCG. "Prove P=NP" would, if worded in the form of a challenge (like in the OP), be ontopic at PPCG. "Find a counterexample to the Riemann Hypothesis" would probably be ontopic at Puzzling. However, both challenges are very well-known (and have very large cash prizes), so it's implausible to think that people would work on the challenges because of PPCG; there's little point in posting them here, as a solution would be major news that went well beyond the boundaries of Stack Exchange.
So in other words, potentially impossible challenges are reasonable, but we should stick to within the scope of what PPCG is reasonably likely to be able to accomplish. In other words, the challenge should be "I'm not sure this is possible, I wonder if anyone else at PPCG has ideas" rather than "I'm not sure this is possible, because a large team of mathematicians has failed to accomplish it for years".