HP does not suggest it, but you can turn off or opt out of the client participation part. Here is a link to HP's view on the matter although it was on 5.3, I suspect it still applies and there bottom line is you should not remove as it may impact other HP apps, so the question you will have is do you care?

http://h10025.www1.hp.com/ewfrf/wc/document?docname=c00564911&cc=uk&dlc=en&lc=en&jumpid=reg_R1002_UKEN#N210

From my experience in removing all of the HP stuff from my system with a couple of exceptions, made no difference, but I do not use HP Image Zone or their CD/DVD burner software. I think I did have to go get the driver for my printer after I removed it but it was a few years ago so I am not sure.

You can download it to some spot on your laptop, then use Add/Remove Programs to remove it, and if it messes anything up, just reinstall it.

You should still be under HP support, I would also just push them in to telling you what it will mess up, if anything.