Hey there - It shouldn't be too difficult. I assume you are concerned less with the physician's response to your request and more with the logistics and security issues, yes? I actually work at USUHS and hooked up a friend from my TPR class last year with a volunteer position on a clinical study run by a physician colleague of mine at a clinic at NNMC, on a fairly high-security base (license will not get you on base, must have military affiliated ID or be "on the list"). He was a civilian with no prior military affiliations, but I believe that it was a fairly easy process to get a security check done and a temp summer pass when the physician took him over to the security office and vouched for him. He really had a great time and got a chance to see what military medical care was like - if you are interested at all in HPSP or USUHS and have the opportunity to shadow a military physician, I would try to go for it!
As a side note, I have been very impressed with USUHS and am applying myself (would never have considered it without my work experience here... never considered the military, or knew it existed).. it is a great school, a very supportive community, the faculty are amazing, and they have some top-notch resources. Just a shout out for good ole USU
