Sure you can! you could even use that specific theme... But, there is only so much you can do with scripting and styling your SmugMug site (like you currently have), the example given would not be possible with this approach.
Something like that would require separate hosting with your own domain (get a package) and typically a free content management system (CMS) running on that. The theme you found is for WordPress, which would be an excellent choice of CMS in most cases. You would have to pay someone to code any and all SmugMug integration you require (pulling of images etc) using the SmugMug API (and probably phpSmug) or RSS/Atom feeds.
You could also roll up your sleeves, learn some basic PHP and have a crack at it on your own like I'm doing now. (There are few things more rewarding than when your code comes together and... just works :)
In reality you would always need to sacrifice (or link back to SM) some functionality though (like the shopping cart) unless you're willing to throw serious time or cash at the problem. But for most people going down this road I guess getting rid of some SM bloat is part of the goal?
Currently there are no themes for any CMS with good SM integration available (free or cheaply) that I know of, but I'd like to be proven wrong. If you can find one, it would offer a flexibility of customization far beyond what the SmugMug site is capable of.
A few, free plugins do exist already for WordPress which may or may not suit your needs, but it could be a start...