Yes;with a large caveat.
Caveat: I don't see a point in other templates that don't have powers. I'd just call it Pure Mortal. If the Pure Mortal wanted a plot where it turned out they had a secret parentage and were willing to change High Concept and template to acquire powers I'd be ok with that.
I'm fairly easy going about stuff if a good reason is presented. I'm also all about keeping stuff simple...so most custom templates would just be Pure Mortals...most likely.
This.
While I haven't gone out of my way to consider the subject, I can't think of a template concept that (a) is sufficiently mundane that it deserves the Pure Mortal bonus AND (b) is sufficiently different from Pure Mortal that it deserves a distinguishing name.
I suppose if you were playing a more Space Dresden version of the game you might have an Alien template, or if you were playing it more Fantasy Dresden-style, you might have Elves and Dwarves and such. Assuming the template was 100% mundane (and didn't have infra-vision or such), then it would qualify for the Pure Mortal bonus. But then, how would it not simply be Pure Mortal with a racial-themed HC?
Do you have something specific in mind? I'd be happy to run it through the Duck Test for you...
Devon/Becq: So would you apply this definition and limitation of no supernatural Aspects for Pure Mortals to any and all Aspects that a Pure Mortal PC has?
Probably. Though as I said, I differentiate between "supernatural you have control over" and "supernatural you are merely associated with". So it's perfectly fine for a Pure Mortal to have "I know a Wizard" aspects and to use the aspect as (for example) an excuse to access Temporary Powers per the rules.
But, again, I'll stress that this is my perspective; if you disagree I'm not going to raid your game and "make you play it right". I might try to evangelize a bit and convert you to my way of thinking, though... Oh, wait, I've already been doing that! :p