Basically yes, but as noted there will probably be some pop riveting involved (I have done this).

I replaced the fabric seats in my Zetec (with autochanger) for some nice special edition leather ones that didn't have the bracket.
For quite a while I just left the autochanger sitting on the floor, it's fairly easy to remove it from the mounting bracket under the seat and the wiring connection is just a plug. But moving the bracket is a bit more than a 5-minute job.

Eventually I decided to tackle it and mount it properly; it was a bit of a battle as the bracket is mounted where the fixings aren't that easy to get at.
I can't remember which was trickiest, getting the bracket off or fitting it back on again, but neither were that easy because there's a fair bit of mechanism that just gets in the way of the tools you use.
IIRC it was basically "just" drilling out pop rivets to get it off and then drilling some new holes and pop riveting it back on.
I think I put it in a "very slightly" different position because my rivet gun couldn't reach the obvious fixing holes. But with the seat off the car you'll work it out.
Remember to place it where you can then get at the fixing screw holes to attach the changer unit.