Well, it is possible, but it depends on the points system if they don't have the caps. The rules section of the EPL gives the breakdown. If you are spending big on a player and paying big wages, then it is. But for prospects, not as much.
Spain has a maximum of 3 non-EU players, but they have an extended list of who counts. Again, see the La Liga rules page for a breakdown. South American players used to (think they still do) get their Spanish citizenship after 2 years, but that's only for those nations, not every one.