The response time isn't crucial.
I suppose at hugely slow speeds, while moving in a straight line, it might work, some of the time, maybe.
But at higher speeds, when trying to do tight turns, after wheel(s) have slipped, and the position/angles are not where they are suppose to be, maybe not.
Anyway, it should be a good learning exercise, either way.
You have got, what 2 cm of clearance, either side when doing turns ?
Perhaps 18 cm - (wall thickness + Micromouse width + initial position error) = Not that much.
So, even small angular/positional errors, can soon mount up, turns are not the easiest of things to do, especially at speed. So, very slow responding sensors, doesn't help.
If it works reliably 90% of the time, that would mean the Micromouse would crash every 10th turn or movement.