Yes, you can remove the string tree. In fact, those tuners are designed so you don't need a string tree, provided you install them in the right order.
My Gear:
American Deluxe HSS Strat
Crate GT212
Vintage '66 Fender Champ Amp
Dunlop Crybaby 535Q
Jekyll & Hyde Ultimate Overdrive
Vintage '74 MXR Script Phase 90
Vintage '77 MXR Flanger
Orange Squeezer (clone)
3 tall pegs and 3 short pegs correct. The short ones are for strings 1-3 and longer ones are for 4-6 correct?