If I remember correctly, the new 24-pin mobos are "required" to work with 20-pin PSUs. It's supposedly in the specification. If you get an adapter it should work.
But, that being said, it should also be noted that some people have had problems. I never put myself in a similar situation, so couldn't tell you personally. As to why they've had problems, can't say. My guess is more of a power output issue than an adapter issue. In anycase, theoritically it "should" work and if u just google, there are many many success stories. One guy supposedly just sawed off (literally) the last 4 pins (no adapter lol) and got it to work.