Yes, but with a couple caveats.
Keep in mind Google Fonts (and any other webfont) isn't yet compatible with major email clients, such as Gmail, Outlook, Yahoo and AOL!
This is why E-goi will only allow you to choose a handful of good old system fonts by default, as those are the ones we know for sure any email client supports.
Still, Google Fonts is indeed compatible with Apple Mail and Android, which come built-in with virtually all smartphones and tablets. If you find that most of your email opens are from these two clients (just segment your contact list for "email client" containing "apple" or "android" and see how many contacts match), it may be worth adding webfonts to your email. This is how:
1) Edit your email's HTML code (either using our Advanced Editor or by uploading your HTML.
2) Enter the CSS code for the webfont you want to use (be careful not to change anything else in the email's HTML). Check out this cool how-to by Email Bakery
And that's basically it! The webfont you've added should now be displayed in your email preview :)