But won't it squeal with high gain?
For my specific PAF, as long as you don't direct it at the speaker - it loves high gain. To my shock, this specific PAF set seems to take on the character of my high gain amps and make each high gain amp more unique in voicing.
Of course you can force it to feedback but its so hard for it to generate the overwhelming feedback we are used to. It functions more like an Ebow when you attempt to obtain feedback. Really strange but I guess that's the magic of a great PAF set.
By the way, I rarely use pedals in front of my amps. So, I never actually used the PAF with an overdrive/distortion pedal going into the lead channel of a high gain amp. So, it might feedback. I go straight into the amp and use the high gain channel.
To my ears, distortion and overdrive sounds better without pedals -- thicker, more dynamic and richer without fizziness -- not to mention noise (but this requires a guitar with hiyaw and a great set of pickups).
Rich sounding guitars when they interact with great sounding high gain amps do not need as much gain because they are so full of harmonics that too much distortion just ruins the sound. Rather, you set at the correct gain and turn up the master to enable the amp to engulf/surround the audience.