Drake on existing 12". enough room for wall tile?

Hi. Im new here and remodeling my baths.

I would like to install a drake on a existing 12" rough in from finished drywall. We would like to install tile on the wall behind the drake. Is there enough space to do this or do I need a 14" toilet?

We have linoleum on the existing floor and would like tile. How do I extend the flange the thickness of the new tile?

Thanks before hand.

The Drake works with 11-1/4"
Maybe even 11"