People with perfect pitch often find out-of-tune notes very disturbing even when played alone. People with relative pitch don't, unless they're played played together with in-tune pitches.
I honestly don't understand why people with perfect pitch hate out of tune music, even when the intervals are correct. I don't have perfect pitch, and I'm glad I don't.
The exact pitch of a note doesn't matter, A 440 is just a choice people made to simplify tuning. There's a need for a standard tuning (for obvious reasons).
Given that A 440 is just an arbitrary choice (440 is not a magic number to our ears), I believe that perfect pitch would be extremely rare and inefficient if there were no standard tuning.
I think it's probable that people with perfect pitch can be negatively affected by always hearing out-of-tune music (especially if their ear is still developing), because the way they developed perfect pitch was through hearing the same exact pitches for an extended period of time (probably in their early childhood).
For people with relative pitch (who aren't trying to develop perfect pitch) tuning doesn't matter, and I shouldn't affect their aural skills at all. If the instrument is not in tune with itself, it's going to be unpleasant, but it's not going to affect your aural skills. In fact it might help you memorize the smaller intervals, and get better a tuning.
P.S : one of my friends is a guitarist who has perfect pitch, but he's not that good at it. It takes him a second or two to guess a note, and gets it right about 80-90% of the time. I used to test him buy playing notes that he would try to guess. One time, I gave him a few notes and he was off a semitone on most of them. The reason, he said, was that he'd been playing his guitar without tuning it for a while and it slowly became a little flat, and his ear got used to it. My guitar however was in tune, so the notes sounded a little sharp to him.