I always take my paper out for paper piecing. I do often leave the block with the paper in tact to use the marked seams when I piece the top together. But then I take it out before sandwiching.
I love PP - it makes it look like I'm a MUCH better piecer than I am! :-)
I'm now venturing into HST and I've found that PP gave me some wonderful scant 1/4" habits. I have a little bit to shore up but compared to last year's piecing I've improved so much!