"On the other hand, it appears that register.com has succeeded in getting federal trademark registrations for "register" and "register.com" despite it being a generic term for the service of domain registrations"
Yah, but look at the goods and services for which they obtained TM registration - "register" is not generic for "email services".
The definition of "generic", as that term is used in trademark law, is much, much narrower than the kinds of things that are blithely deemed "generic" in these discussions, but I'm not up to re-hashing that whole discussion.
"What happens if and when you get a TM on GourmetTurkeys.com"
If you "get a TM" on X, then you have a TM on X. I don't understand the question.
The dividing line between generic and descriptive is very critical, because descriptive terms may be considered to be trademarks upon a showing that the term has acquired secondary meaning as a trademark - through such evidence as longtime use, advertising expenditures, consumer surveys, etc. Is that entire subject likely relevant to someone who has just registered a domain name, and now wants to know how to "TM a domain name"? Probably not.
Does one single-member NAF case prove much? Also probably not. UDRP cases in general are lousy reference materials to learn about trademark law. In the register.com case, for example, attacking the legitimacy of a federal registration, rather than moving much of the same argument into the legitimate rights / bad faith sections, is usually a tactical error.