No. Teamwork says "immediately". When something triggers multiple effects (like the end of a turn), the immediate effects take place before the non-immediate effects. The door control effects (including the regular door check) are non-immediate effects.
Glossary:
Quote:An immediate action takes place instantly under a particular set of circumstances, even if it is not the character’s turn. This action can interrupt other actions, taking effect just before they do. If multiple immediate actions take place at the same time, the acting player takes any immediate actions, then the player to the left, and so on.
http://www.bloomilk.com/Glossary?Id=29(As an aside... "immediately
before X" works differently. If two effects trigger "
before event Y", the immediate effect takes place after the non-immediate effect. What is consistent between "immediately before" and "immediately after" is that in both cases the immediate effects are closest to the to the triggering event. I just mention this because I only recently learned about that "immediately before" detail myself.)