Can PhD students take a semester or two to study abroad, similar in nature to a sabbatical?
This is really commonplace in my field (computer science). I spent every summer of my PhD interning somewhere.
I think that this is ultimately up to you and your advisor to figure out, as well as for your university/the host university to agree to (universities have rules regarding how much time you need to be on campus, and about double enrollments). If it's one semester then it should probably be fine. I don't know about the standards in other fields, but spending a whole year away is less commonplace (I would probably not agree to it myself as an advisor).