I fold my tower with the bimini on there. My tower folds back so it's a bit of a pain. Your tower folds forward so I'd expect you could just leave it on there with the rear and middle bows attached to your rear tower legs.
Just so you know what you're getting into here's how you fold it:
1) disconnect both sides of the tensioning bow (Middle bow)
2) Remove the two thumb screws from the front bow and try not to drop them in the water if the boat is still on the water.
3) During the process the front bow will seem like it's stable and stuck in the brackets so you briefly divert your attention elsewhere and it suddenly pops loose and hits the person in the observers seat on the head. Ha! I mention this because I've done it numerous times.
4) Bring the front bow to the middle and then both to the rear bow.
5) Wrap the front bow around the middle and rear bows a few times. Otherwise there's so much excess fabric to deal with it will be difficult to get the boot on.
6) Reconnect the tensioning bow legs to the rear post of the tower.
7) Put the boot on
Deploying it is pretty much the reverse.
Between steps 4 and 5 things are flailing around a bit because only the rear bow is attached to the tower so it can obviously pivot freely.