I`m only speaking out my thoughts here, since I don`t know the thoughts of American recruiters, but at least I can guess.
First, I think, you wanna decide what you really want. A degree in Archeology might let recruiters think - wow, he`s got a degree in Archeology, but nothing more. Honestly, I doubt that it will give you any benefit if you really think about working in EMS fulltime and building a career there. Sure, it might be interesting (tell me about it, I`ve planned to study Archeology or History for the most part of my teens - just where did I go astray??? ), but it might be - and I`m doing this in captions for a good reason - a "timewaste" if you think your future lies in EMS...?!
I just imagine, that if you`ve undergone a study in a certain subject - you wouldn`t want it to be just Plan-B.
It certainly wouldn`t do you any good with your dreams of being a SWAT-Medic (search for some threads here,ít`s really hard to become one).
After school I planned to study medicine, but somehow got into EMS first, now I`m thinking moving to Britain to study Paramedic Science.
My recommendation: Inform yourself about the subjects (EMS as well as your possible future degree, may it be Archeology or something else) very thoroughly, try to decide what you really want, weigh up your options - and then just do what you feel most comfortable with.
Just my humble thoughts...
P.S.: I think after a certain amount of time it isn`t possible anymore to edit posts.