Hardly IMO, because TGUs don't follow the usual rules for sets and reps.
As Pavel describes it in S&S just one TGU equals about 8 reps for another exercise like the bench press.
Because of that doing e.g. sets of 5 in the TGU would be the same as doing sets of 40 in the bench press. That has nothing to do with strength training anymore.
Because of that a triple progression doesn't really work, but a double progression of adding reps and then weight is a viable option.
How to Get Better at Everything by Training Multiple Get-Ups and
How to Properly Program the Get-up for 3 Different Goals might help you out.