Is auditing graduate physics courses (officially or unoffically) a viable way to eventually get into a PhD program? I am considering a possibly risky route into graduate school. Namely, auditing classes at the university I would like to attend and then reapplying after a semester or two. This way I can demonstrate my abilities directly.
I cannot speak for Physics, but I can speak generally. Generally, auditing courses is unlikely to get you noticed in any way and is unlikely to generate the sort of information that the admissions committee will value. I cannot assume that you will be able to develop the connections that you desire because I doubt such opportunities will be available via auditing classes.

In my field (though perhaps not Physics I warn) a way forward with a poor undergraduate result but a desire to do a US-based PhD is to do a one-year master's in the UK or Europe, and to do extremely well in that programme. Via this route you show that you are able to complete very high level coursework and, further, are able to produce actual research (in the form of a master's dissertation). These are much better indicators of PhD success than audited classes or GRE scores. Also, if you have, say, a UK distinction in your master's, in your PhD statement of purpose you can address your poor undergraduate performance head on: say you were dealing with personal circumstances but your demonstrable success in the higher degree programme evidences your abilities to succeed at real research. 

In other words, you are giving them real evidence of your commitment and abilities, while auditing doesn't do that.