If you fertilize just the right amount every time, it is not necessary. It is hard to do this practically, however.
One advantage to water first is that you will rinse out a good bit of any accumulated salts from the last time you fertilized. So if you fertilize maybe a bit too much for whatever reason, if it doesn't rain in between, then next time you fertilize you could get to a point where the soil has too much fertilizer in it and it starts to inhibit the plant.
Depends on how much rain you get, how often you fertilize, how strong your fertilizer is, what fertilizer ratio you use, etc. If you use a 10-10-10 type fertilizer, this will have too much P relative to N, which will accumulate in the soil if it doesn't get rinsed out by rain or watering.