My questions is, does this file get executed when browsing from the
front end?
Well, yes and no.
Your file will be included on the front end when using the theme in question, but as your code is hooked to admin-only hooks, nothing really executes. The file is read but the code doesn’t do anything except on the backend so all you’ve really done is used a 10,000ths of a second (if that) and a trivial amount of memory. I very much doubt you will notice the difference. The hooks should take care of the problem without your doing anything special.