The rate of detoxification might be increased yes.
The detoxification system is a series of steps controlled by enzymes and some of these enzymes might be increasingly expressed during water restriction (for example, CYP3A4 is an example of such an enzyme).
In my understanding, water soluble toxins can be excreted at all times (which means they might not be subject to accumulation) but fat soluble toxins needs to be transformed in water soluble ones (via these enzymes) before they can be excreted.
So a lack of water might impede excretion of recently produced water soluble toxins but not necessarily the detoxification of fat soluble toxins.