And I would be more worried about severe failures at that point. The OP was asking about the need to buy a specific BCG. If the rest of the upper is assembled right, he should be good to go. Manufactures sell complete uppers MINUS BCG's every minute of the day (like the one in the OP) and buyers drop in off-the-shelf BCG's with no issues.
@the OP, you did fine with your choices. Enjoy that rifle!
@the OP, you did fine with your choices. Enjoy that rifle!