I don't see why not. I seem to recall reading something somewhere about purchasing from neighboring states but I don't recall the details. Though I guess it all depends on whether it's a private sale or from a dealer. Worst case scenario I guess is that you have the seller send it to a local dealer who will then "transfer" it to you?
I believe if you buy privately in Texas (for example), then you technically need a TX ID--though I also suppose that depends on how "private" the sale is. ;-)
BTW, you wouldn't happen to be the Aussie subject of the SAF lawsuit regarding the NM CHL citizenship requirements would you? Just curious :-)
Edit: I think this may have been what I read on the neighboring states thing: