Is it proper to follow up a mailed resume with a phone call, and, if so, how soon?

If I were you, I would have the letter include a signed confirmation. That way you will know when it gets there and also that they have actually received it. Then follow-up within 24 hours to make a brief presentation about yourself. I guarantee no one else will do this and you can set yourself apart from the competition.

Make sure the original job posting did not say "No phone calls." Otherwise, you are going against the wishes of the company.

Make your call VERY brief and very polite -- simply a verification that your resume has been received. Many jobs receive hundreds of applications for a job, and you should assume that many of those people are also calling -- the last thing you want is to be annoying.

give the proper amount of mailing time probably one week and then do a follow up through phone...