I think it depends on the anthology? Certainly, many of them want rights to "exclusive" publication within that time limit, or to "first" publication, and it depends a lot on the power balance between the editors and the authors (and how ethical the editors are being) but all of that's really shifting right now anyway as people figure out how things like blog posting fit into the "publication" paradigm anyway. With a fanwork anthology I don't have the first idea, since the copyright issues there would be complicated anyway; I wouldn't be surprised if they tend to be more restrictive than average, but most of the current ones commission work specifically for the anthologies, I think, though some of the early ST and SW ones I'm pretty sure reprinted some fan-published work. (I should ask someone who's actually been published in an authorized fan anthology!)