So I'm in my last year and I've never MSAF'd anything, so I'm not really sure about all this... Is it really a get out of jail free, the professor won't care?

I have an assignment (worth 15%) due tomorrow for a 3rd year class and I'm probably not going to be able to get it done. From what I understand, if I MSAF it, I'll just get a couple day extension, which is fine, but I'm concerned that I'll have to explain myself to the prof and wondering if it might not be better just to take the late penalty.

Technically no you shouldn't - though they might ask why, they shouldn't ask for documentation or anything. However, there is the rare prof who will give you trouble - I only encountered one while I was at Mac (though I did have another prof give the entire class an extension in protest). In the vast majority of cases though, you should be fine.