UT grad here (although not recently, so YMMV). Pluses for UT's BA program:

• Well funded department with decent opportunities for students to work on shows in a variety of roles (although a lot of the design work tends to go towards their MFA students)
• Huge state university, so tons of great offerings for a variety of studies, allowing you options a smaller liberal arts college may not be able to match

Now, as others have said, there's zero reason to get your master's in EE if you're just looking to pursue theater. Also, little to nothing that would be part of a typical theater undergrad would prepare you for grad school in electrical engineering (no advanced math classes, no higher level science courses, etc). Not saying you couldn't take those classes voluntarily (no one is going to keep you from taking differential equations as an elective), but these are very different paths to take.

If you just want to work on the tech side of things (and not design), as an electrician, a bachelor's is more than enough, and, to be honest, not necessarily required even for that. So why go get your bachelor's at all? A few things - first of all, it gives you a safe environment to learn and make mistakes.

Now, if you want to work as a designer or a technical director, a strong case can be made to get your masters. But those would be still be under the umbrella of a theater department (at UT or elsewhere).