I wonder if that plumbing set-up violates any waste/water by-laws?
The sort of thing where it's mandatory to have a 1 or 2 inch air gap between a tap and the maximum level a sink can be filled to.

The bath ought to be fitted with a one-way valve to prevent waste water getting back into the tub..I just don't know of the top of my head if it's legal or not, but by the sound of it it's a pretty rank set up.

I'd get a plunger and keep it on standby :)