No, Tower has final authority over which runway to use.
- Tower controllers have direct line-of-sight with the runway.
- Tower has better knowledge about equipment outages, obstacles and other special situations happening on or around the runway.
- Tower is the one who is granting landing clearances. They have authority to reject planes that are coming in from the wrong direction.
The job of Terminal Control is to "pass" the airplane to Tower. From that point onwards, the responsibility of Terminal Control has ended; Tower will direct the plane until it leaves Tower's responsibility (miss approached / on the ground). For example, a pilot can approach an airport with an published instrument approach, then circle to land on a different runway. The runway is located at the airport. Therefore the responsibility lies with whoever has control at the airport, not the surrounding airspace. The airspace directly at the airport belongs to Tower, not Terminal Control.
Your concern of conflicting traffic is, to a certain extend, invalid, because they have been addressed by the airport designers. See, for example, the approach for VMMC:
- The approach begins from the South or South West. An approach from the East would have conflicted 07 approaches for VHHH.
- Missed approach requires a climb to at least 5,500 feet. That keeps the plane separated vertically from departing or arriving traffic at the West of VHHH.
For reference, 07R approach for VHHH:
You can find similar cases for airports like KLAX, KJFK and EGLL.