Hi Danny and Amy!
I wasn't born with perfect pitch, but have developed it to an extent through musical studies (if someone plays a G chord I can spot it immediately etc). I can say that noises or music are definitely not overwhelming for me - I have the ability to work well in both absolute silence or with loud music/noises around, it just depends on my mood at the time whether I will prefer noise or silence.

When I get really engrossed in what I'm working on, it makes no difference to me, I'm just in my own little world. Being able to identify
In my studies and musical gigs I also met a few people who possessed perfect pitch, both in-born and taught later in life, none of whom expressed any inability to concentrate due to noise. If anything, they generally seemed to prefer having some soft music playing in the background or having a TV on with the volume down while they studied, to avoid the awkward absence of any sound.
Personally, I think it boils down to the individual more than anything.
Shuki