I don't think bringing up BTTF makes that part of the ending any better. BTTF actually sets that element to time travel up fairly early on, and it becomes an integral element to the plot, with Marty's whole existential race to the clock to make sure he's born.
The finale didn't set anything like that up, and if she was going to die, it should've been when she collapsed after Aku's death. Her hanging on long after that until their wedding of all things still seems like some lazy writing to inject some last-minute sadness into the ending. Just because BTTF did it doesn't mean Samurai Jack can do the same thing without any context behind it.
I mean, yeah, time shenanigans and all that, but even under BTTF rules, Ashi should've already been long dead. I think. Man, time travel is such bullshit.