Do arxiv papers matter at all while applying for a doctoral program in Physics?
Yes, they might be a benefit, but, since they aren't refereed, it might be limited unless it they are remarkable in some way. If they are also submitted to a journal as well, then it would be worth more.
It would, however, require people examining your application to take a look at the papers and make some judgement. They might be willing to do this, or not. They might be impressed, or not, depending on what you have there.
But, as you suggest, self-study, and especially research have value for doctoral applications.