According to the leaked achievement list, there is an MP achievement. I suspect there will be more than one in the final list.
On the FAQ they responded about the leak achievement and said there aren't achievements MP related.
So far, MP sounds fine. There's basically no connection between the two, from what they said (while for ME3 they announced the GR from the start).
I'll probably try it...though I don't know when. I doubt I'll stop playing the SP during the first run.
My major problems with ME3 weren't caused by MP (while I didn't like at all the bonus ending, I'd have still disliked the endings without it, and the autodialogue was still my major problem) so I'm not that bothered, as long as what they said about the non relation between the two modes is real.