I'm always giving my acrylic knit sweaters haircuts. I find that they start to pill quite fast (not that I'm using any good acrylic or anything) but I don't think it will pill forever. If memory serves me right, the pilling stops after a while.
When I do my 'haircuts', I usually make sure I have really good lighting so that I don't accidentally snip the yarn... I don't what to have to fill in a hole
I use tiny sharp thread scissors and sort of skim them along the top, and hold the fuzz in my other hand to bring it out of the flat surface and then only cut at the edge of my fingers. So far, I've not nicked anything.