Should all references to a text domain be to my current theme?

You can remove all the translation references if you don’t plan on translating it. You can also leave it in place, it shouldn’t hurt anything..

If you want to remove it, go through your theme files and find references to __(' Your Text', 'Domain') and just change it to the “Your Text” portion. (Sometimes, you may even see _e('Your Text, 'Domain')).