Zack, that's not dangerous or even foolish thinking. After all, if a prebuilt computer has a free pci-e slot for a GPU card, putting one in wouldn't do any harm. In theory, if there's a fitting slot for a component, any component fitting to that slot should work. Theoretically...
But before doing that, remember that a in prebuilt rig the PSU mostly doesn't have the extra power needed for a gaming video card. As Silver said, it's not far from building the whole computer yourself. On the other hand, I've seen some prebuilds costing far less than it's components bought separately. If you're looking at a really tempting bargain, put the specs into
this PSU calculator to see, if the El Cheapo has the power for your GPU.