If anything you would be more likely to enjoy it as a total newbie... Because while the movie is enjoyable enough, it's... not very Star Trek-y. And I say this as someone who's only a casual fan of the franchise at best. (Meaning, I have seen most of the movies with Kirk's crew, skipping 1 and 5 because I heard they kinda blow, and I've also seen some of TNG, and while I've liked what I've seen of it well enough, I wouldn't consider myself a hardcore Trekkie or anything.)
As for the trailer... Yeah this looks just as non-Star Trek-y as the previous one was, if not more so. Still probably gonna go see it though... Though I imagine I'll have a hard time seeing the bad guy as anything other than "Evil Sherlock Holmes".