an unpotted pickup has a slightly deeper bass, and a more complex/3D midrange...
as for an unpotted APH-1, it's up to you...if you don't go crazy with the gain and/or don't mind the feedback go for it! Thefeedback is not to bad but it will feedback more that a potted version.
I have a feeing that not potting an over wound/super hot pickup like an Invader might not be any different that a potted one. The tonal changes from potted to not potted are pretty subtle and I just have a feeling that you might never notice it on an Invader.