Get gravatar preferences in functions.php

Hi,
on my theme I’ve wrote a funcion (read here on the forum) to do a check on the existence of a gravatar for comment users. Since it’s quite time- and band-consuming, I’d like to avoid running it whenever possible.
To be more precise, I want to run it only if wordpress has gravatars enabled and the option set for the fallback gravatar is “empty” (I don’t know if this is the word used in English since I’ve my wordpress translated in Italian, anyway is the option below Mistery man).
Does wordpress expose variables for these two preferences, or I have to do a SQL query?