Purely anecdotally, I do not think it does, for two reason:
- If it did stack, then you would have a pretty decent chance to max out attack speed. 1 in 225 shots will start a chain of two consequitive procs, and more importantly after a single one, you'd have the full 15% chance to get it on the next. Wouldn't be that unlikely you'd get 4 or 5 procs in 10 seconds, especially with making closer and closer to two shots a second.
- More likely however, is that the buff is simply a unique effect, as many are. This isn't evidence, but I think a fairly decent assumption.
I am rather more curious if procs while the buff is up extend the duration, or if only procs after the buff is gone will retrigger the effect.