I think it could've gone either way. As things actually are, I think The Batman already did suffer from a sense of Batman burnout. In that respect, coming out soon after Rises with no Batfleck in between might actually have made it *more* succesful. Of course, it also wouldn't have looked quite as shiny to some people if placed that close to the Nolan trilogy.
Regardless, though, there would remain one massively importance difference between this and ASM, even discounting the quality issue:
ASM was a reboot nobody wanted. As in, the studio actively canceled the ongoing series people liked in order to reboot. At least in the Batman hypothetical, Nolan ended his movies on his own terms and simply didn't give the studio the option of continuing them in any meaningful way. The Batman might have been found wanting by a world still high on Nolan's work, but it wouldn't have borne the same level of resentment that ASM got saddled with.