Yes. If you want to use that font, then you have to check the headerinclude template as well. There will be a link something like this:
<link href='https://fonts.googleapis.com/css?family=Exo+2' rel='stylesheet' type='text/css'>
You need to copy that over into the headerinclude of the theme where you want to use the font.
<link href='https://fonts.googleapis.com/css?family=Exo+2' rel='stylesheet' type='text/css'>
You need to copy that over into the headerinclude of the theme where you want to use the font.
What goes around comes around