In theory you should be able to do this, but I expect in practice it is such a complex system that you couldn't faithfully model the tides by looking at the bat

In theory you should be able to do this, but I expect in practice it is such a complex system that you couldn't faithfully model the tides by looking at the bathymetry. It's one of those problems where everything affects everything. It's a gigantic pool of liquid, so you'd have to model the entire ocean. For many areas you'd need to be taking into account how the shape of the coastline itself changes with the tide as well. Computationally extremely complex to do it this way.