I'm assuming you mean people within a project, who upon source code checkin, are required to have either requested a code review or completed a code review first?
No, Teamreview does not stop checkins. (In my mind it would be more of a custom checkin policy specific to a project/site.)
Do you utilise shelvesets in the interim? (ie. coder shelves changes until review completed, then has approval to checkin).
If my assumptions above are incorrect, explain what you mean by >>"supposed to do a code review?" << , ie. :-
1) A reviewer who creates the "New Code Item" or
2) a coder who replays the Code Review Item and makes changes to source code as a result of a code review?
A reviewer is potentially anyone in a project team. Team review doesn't impose any limitation on who can create a review.