In FMA1 at least, he can't swim.
And, naturally, it would be very odd if he indeed could swim, as both his leg and arm would definitely weigh him down. Whether the automail is rust-resistent or not; I don't think that has anything to do with the question if he is able
to swim. It'd just be a matter of how well he takes care of his 'machinery'.
And if he can swim wearing the Briggs automail, well, I guess it's debatable. But I still don't see Ed keeping his head above the surface, not before getting his real body back anyway ^^
And, I think it's possible that both Ed and Al learned to swim before the accident; there's at least a few streams and small rivers in the area of Resembool, as evident in some of the anime(s) episodes. I remember in particular one part from FMA1 where we're told how Ed would always find Al by the bank of the river after they'd had a fight. But again, that's anime
But there's also THIS
page from the manga.