Do arxiv papers matter at all while applying for a doctoral program in Physics? Consider an applicant in a Master's program with a fairly good application in terms of LORs, GPA, research background, and standard tests. If this applicant, who is applying to a doctoral program in Physics in the US, also has a collection of writings in arxiv would this add any more value to the application?
In other words, can arxiv papers boost an application's value in any way since they might show the self-study activities of a student?
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.