Nope. The idea, I'm assuming, is that changing the pillow case gets rid of bacteria that can cause acne. Unfortunately, those bacteria already colonize your skin so it won't make a difference. Or could it be that your pillow case has residue from the products you use? Again, not really likely because the amounts would be so small compared to what your'e already slathering on your face.
I just saw the FutureDerm response. They did a better job in answering this question than we did because they raised some good points about fabric softener and other "stuff" that's on your pillow that could contribute to acne. So, based on this additional information we're reversing our stance on this: If you're having trouble with acne it makes a lot of sense to change your pillowcase more often.