I live in California, so I don't have the foggiest idea of how difficult it would be to register/license your car there. In fact, I don't know anybody here in Northern California (North of Sacramento) that owns a GTM either. I hear rumors of a couple, but nobody has jumped out and identified themselves as being close to where I live. However, between this forum and the factory five cars forum, I'm always surprised to see how many people drop in and send invites to other to come see their car. The last time I checked, GTMs are more heavily populated on the east coast than the west. I'm making the deduction that it has a lot to do with the location of the factory. Curiously, there are quite a few in Texas as well... LOL.
Regarding your skill level .... well ....I was headed to medical school and thought I would do well there due to having a strong mechanical background. I decided against it due to the financial burden it would have placed on me. (all those MCAT study hours went to waste). I've been working on cars for 30 years now, and I often think of the human body as sharing similar mechanics. As a physician, I'm sure you have the same deductive reason skills and the ability to research answers to perplexing problems. Does that necessarily translate into having the artistic ability to complete the build? *shrug* ...not for me to say really. My body/paint guy gives me hell for overanalyzing things before I do anything to the car. He is the type that can just make stuff work by doing it (often many times over). Regardless, the GTM is certainly a project that I feel requires a little bit of both approaches. You do have an instruction manual to guide you through the build, but remember that these cars are not something that you can just assemble. I've been told by a couple forum members here that I should ignore parts of the manual anyways. A lot of people say that the GTM is one of the more difficult kits to build. (see crash's response as well).
Personally, I would never want to discourage anyone from tackling a challenging project that they are going to love. With enough time and money, you can really do anything you want. For myself, I'm pretty good with mechanical stuff. Body work? Well, that's an art form, and I absolutely suck at it. I can work materials, make parts fit, shape things, and do all the basic work up through the first primer. After that though, the fine details that make a project professionally complete must be done by someone else who has the skill and talent. I will most likely spend a good portion of my budget paying someone else to complete the final prep, paint, and polish. In regards to the skill of building the gokart portion of the project, I feel that drilling, riveting panels, and bolting things up is pretty straight forward. At least until you run into the panels that are suppose to fit, but don't without modification. No biggie though ... there's a tool for everything.
You can get into the car as deep as you want, and the forums here are a wealth of knowledge for "fixes" to many of the common problems that will be encountered with the build. As crash stated though, experience will generally yield a better product. (see my paint and bodywork statement above) I think that there is a lot of truth to the statement, "If it was easy to build a GTM, everyone would be building them." I also believe there are many levels of "fun" when building a car that vary from person to person. It is impressive to see how deep people get with this GTM build. Looking through the various build threads, some guys go WAYYY beyond the typical assemble job to make their car custom, and with their own signature in the design. If you decide to build a GTM, your skill level is going to dictate how comfortable you get with making the car "your own". If you just build it as it comes from the factory, then the final product is going to look pretty similar to that of the factory kit. Looking through all the build logs here, and hundreds of pictures of other builds, I feel that the car needs a little bit more of a personal touch to take it to the next level.
I wouldn't let your lack of knowledge prevent you from building a GTM, as parts of the build are pretty easy mechanically. Just be prepared for the not-so-easy things to consume a large amount of time and cursing. Without the experience, the build may take longer than you expect. There are definitely areas of the build in which I will be soliciting the expertise of others.