The correct answer to the original question has been given many times in this thread.
In my experience however, there are plenty of pilots, some "old and experienced" that would have answered this question INCORRECTLY.
In the case of a downwind turn in a steady airmass the IAS will stay the same ...
Only in theory does there exist such a thing as "steady air mass"
AerocatS2A 
The answer to the conveyor belt question is, NO - the aircraft cannot take off.