The quick answer is -- yes, it will explode.
Nearly all explosives carry both reaction
components (or an unstable single component like
TNT). Effectively, all they need to react is a
warm enough temperature and a suitable trigger. On the other hand, without an atmosphere to conduct sound and shock waves, an explosion is silent until the actual debris,ejected from the explosion hit. Thus, the characteristics of damage are substantially different.
It is also true that regular bullets will fire from cartridges in space -- Apollo astronauts used a "thumper" which fired such shells to act a sources for seismic studies of the Moon...Since there is no air to slow or deflect it, a bullet in space hits just as hard no matter how far it travels, (unless you are in a gravity well-- then it picks up a lot of additional energy).