My gut feeling on this is "no". I see MO as more for questions where one expects that someone will be able to give a definite answer. In your example, you are going in with the expectation that no-one else will be able to answer your question. So I don't think that MO is the right place.

I think I agree with Andrew and Scott. My gut reaction is that a polymath question will be very regularly answered and edited so it might be getting bumped to the top too much. But I might very well be wrong. I think asking the smaller sub-problems instead, and keeping the main polymath project on a blog somewhere. But as I say, I might be wrong and perhaps the best thing to do is to ask the question, and if it doesn't work we'll learn from the experience.

@Max Muller: the polymath thoughts you're having were pretty much similar to the ones I had when I posted that "let's compute the Fourier expansion..." question. I invited Gowers to give a colloquium at my university on the polymath stuff a couple of months ago and the idea had been kicking around in my mind ever since. But I agree with the other posters here---I don't think MO is particularly optimised for this sort of thing---it has big visibility (so e.g. if I'd just posted my question on some blog or other then it would have been even less likely to have been answered) but it has disadvantages too. Very early on junkie made it clear that he'd be able to do the problem, and the moment I realised this I just told him all I knew and then he did it. It was only a computational problem anyway---I knew the algorithm but had tried and failed to implement it and debugging was hard because my program output a plausible sequence of numbers which I knew were wrong but it was hard to pinpoint exactly why it was wrong. So it was just a case of getting someone else to do it. Not really polymath then---but I was very grateful to junkie for doing it! I'd thank him in person if I knew who he was :-) But what was tough was that when he had an idea he'd post it but it would end up as an "answer" and it wasn't really an answer and there was no real point voting for/against it, and voting just jumbled up the order of things anyway, which was hardly the best idea. Somehow perhaps my main point is: what would one vote for, and how does one stop voting from disrupting the natural flow of the argument? One can't do this. Hence for a big project I can't imagine MO working well. The advantage of what I suggested was that it was shortish so it worked---but basically one or two people were enough to nail it. If the problem had been harder it just would have been a lot more chaotic: already when I posted I knew how to do it, it was just that I didn't have the time to do it (and had already tried and failed due to making an error which I couldn't find) and someone else did!

@Max,

please don't ask a single question (i.e. mathoverflow page) with several 'actual questions' on it. Ask separate mathoverflow questions for each sub-problem. Remember, questions should be as specific as possible (but not more so!) and you should ask every question with an earnest hope of being able to accept a single answer that you feel makes any other answers redundant.

(You'll notice that this desideratum makes all [big-list] questions bad questions, but I think that's compatible with my view of [big-list] questions! :-)