Short question: If I switch to a wider tire, do I also need to change out my wheels/rims?

Longer details: I have a Specialized Sirrus which was sold to me as a hybrid. I mostly ride it on roads, but occasionally take it onto easy trails. I am quite happy with it, except that it has rather poor traction if the trail is a little muddy. Up to now, it has had the original "All Condition" 700x32c tires on it. However today, while replacing the tube, I evidently flubbed the job and tore out part of the bead. Now I'm in the market for new tires. For a while now, I have had my eye on tires that are a little knobbier on the sides but still fairly smooth down the center, such as the Specialized Borough Armadillo. However, this is a slightly wider tire (45mm instead of 32mm). Can I reasonably expect to put this wider tire on the same wheels, or do I need to replace the wheels if I switch to this wider tire? As far as I can tell, the current rim width is 24mm.

As a side note, I am rather disappointed in these Kevlar "armadillo" puncture resistant tires. Every time I spring a leak (which is often), I find myself pulling out three or four chips of stone that have become embedded in the tire.