Is there any evidence that JS Bach, A Vivaldi and/or J Handel had perfect pitch? Perhaps, if one can devote so much time and energy to music, he would develop such abilities.
Today we have digital tuners and we agree that all instruments are tuned to A = 440 cycles per second. There were no such standards in those days.
I doubt any of them would have perfect pitch in the modern sense of the term, because every church they went into would have a pipe organ tuned to a different reference pitch. Furthermore in that time, pipe organs and vocal choirs and brass instruments all had different reference pitches. And reference pitches, to the extent that they existed, would be different depending on what nation or region you were in at the moment. So to have perfect pitch in the modern sense would be very confusing to a musician in their time.
As Laurence alludes to, when discussing "perfect" pitch, there is a difference between relative pitch and absolute pitch.
Relative pitch -- knowing where a pitch falls within the context of a scale, and hearing the purity of intervals (rather than individual pitches) -- can be learned relatively easily, through exposure to music, and most musicians probably end up developing it to some extent, even if only instinctively. In fact, for vocalists, string players, and trombonists, relative pitch is an extremely important aspect of performance. The composers you listed above certainly would have had a strong sense of relative pitch, if for no reason other than all of them were violinists.
As for absolute pitch -- recognizing individual pitches without the need for a reference pitch -- your question seems to revolve around whether or not this ability can be "developed" by spending so much time and effort on music. To my knowledge, there is differing opinions about how well it can be trained -- especially after childhood -- and how useful such hypothetical training actually is in practice. See: Is there a way to develop "Perfect Pitch"?
I am not aware of any evidence that any of these three musicians had perfect pitch (though it wouldn't necessarily surprise me, either). What is more interesting to me, is asking how the phenomenon of perfect pitch would have even manifested in the Baroque Era. This was a time before any standardized reference pitch (A=415 is just a modern compromise, not an actual period standard), so pitches could vary wildly (as much as a minor third!) from region to region, or even between two church organs in the same town. IIRC, I think Bach is known to have written organ parts in a different key from that for the choir and orchestra.
How could someone with perfect absolute pitch even perceive pitch names in such an environment? Edit: By which I mean, any attempt by the mind to create some sort of mapping between letter names to specific frequencies would have been foiled by the widespread fluidity of such pitch assignments.