The Doc specifically mentions that Mr Fusion only powers the time circuits, not the rest of the car. So to get Back to the Present it would have had to have been functional, given the plutonium system was removed between BTTF1 and BTTF2.
Mr Fusion at least had to have been working. Otherwise in 1885 they wouldn't have been able to power the time circuits. That said, that doesn't mean the flying cart upgrades were still.