Pods can do physicals.
You will certainly learn and do full H&Ps in physical diagnosis class/lab as well as 3rd and 4th year rotations. Some residencies are really big on having pods medically manage their patients... usually they are the big academic teaching hospitals. Whether DPMs can bill for it or not is another story, and that varies from state to state. They can certainly always bill for a podiatry workup and the H&P of a F&A complaint.
My question for you is: "why do you want to do a full H&P?"
A full head-to-toe physical takes a really long time (and even longer to write it up). I'd much rather do a focused H&P... you should go to pod school because you want to be a F&A specialist IMO. A generalist's job is to know a little bit about many things and be great at H&Ps. A pod's job is to know a ton about F&A, a fair amount about systemic diseases that affect the foot, and a little little bit about everything else. I think full initial H&P can usually be left to the docs who do dozens of them every day. Regardless of degree or area of specialty, you sure won't find very many specialists who do complete H&Ps; you don't see a psychiatrist or a OB/GYN performing Rinne and Weber tests.
In podiatry, most of your patients will be referred to you from IM/FP where they got a full physical and were turfed to podiatry for diagnosis and treatment. You can scan the results of the H&P, and then you typically do a focused podiatry physical (derm/nail, neuro, vascular, and musculosk of LE... sometimes biomechanics).
If you get a new patient or work out in the sticks where doctors are few and far between, then yes, you could do a full H&P, but you'd usually still focus it at least somewhat to their podiatry complaint that brought them into your office. As a student, you always want to be thourough, but you usually don't have an hour for each patient to be listening to lungs, asking about hobbies, and jotting down childhood immunizations. Pre-op is one exception where a good full physical is very valuable.