...Shana is arc-driven rather than episodic, so there are characters in the later parts of the anime series' first season that are bound to return in significant roles sooner or later in the second season. (Having watched episode 1 of SnS II, I can think of a couple of characters whose presence would be more or less inexplicable to a total novice.) As a result, you'll probably miss some of these characters altogether if you jump straight from the first manga volume into SnS II, and even assuming some level of recap down the road, there's a good chance you'll be left wondering about the appearances, backgrounds, and motivations of several key players in Shana's universe.
If you haven't seen the first season, I would highly recommend that you watch at least the movie: it takes an hour and a half to retell the events of the first six episodes, and you'll be able to familiarize yourself with the protagonists and some of the basic workings of the world. Be mindful, however, that the end of the movie is merely the
beginning of the Shana story; to fill in all the blanks, you'll need to know what happens between the end of the movie and the beginning of SnS II, a span of several books in the light novel series and eighteen episodes, less filler, of the anime. It's an awful lot to gloss over, and I think you'll enjoy the second season more if you watch the first season to get even a general sense of everything that's happened thus far. Besides, the first season is enjoyable in its own right.
edit: I don't mean to say that watching the series through is the only way to catch up on the story, especially since Shana exists in several types of media. Reading the novels would be another solution, as would reading as much of the manga as has been released, as would finding a synopsis. It does make a certain sense to watch the first anime season as a natural precursor to the second--all of the adaptations differ from one another, so you'll find some disjoint amongst novel, manga and anime--but in any case I'm just trying to advocate the idea that the more you know, the better prepared you'll be.