Er, well, sort of. The electromagnetic force between two electrons pushes them apart, but if you apply enough force, you can overcome this repulsion. Doing so, you can get past the electrons, and force the cores of the atoms closer together. Of course, then you've got protons pushing each other apart, and their push is even stronger; but, again, with enough force, you can get past that. At this point, you get to atomic cores interacting directly with one another, and now things get really messy.

But yeah, in any case, particle accelerators do more than make atoms touch one another, they get atoms all mixed up with one another. (Thus the other common term for a particle accelerator is an "Atom Smasher". )