This is actually a bit more complicated to explain and I don't think there is a clear yes or no answer. Here's what happens when you consume coffee (or more precisely, caffeine):
The caffeine acts as a diuretic and withdraws water from the body. The body reacts to the dehydration with increased ADH production which leads to less water being excreted by the kidneys. As a result, the urine becomes more concentrated and ensures that in the case of OAB you have to go to the toilet more often - but excrete less. This is because concentrated urine irritates the bladder more. Thus coffee is first of all a clear trigger for OAB. Whether the bladder becomes smaller in the end depends of course on many other factors - but generally speaking there is a risk of bladder shrinkage with OAB. To a certain extent, this is a vicious circle that one tries to counteract through bladder training.
In general, one can only say that it is not a good idea to drink a lot of coffee with OAB. The same applies to highly acidic beverages (e.g. orange juice) or hot spices.