Is it possible to finish a theatre-engineering double major in four years?

Yes it is possible if you go to summer school to pick up some of the units. I went to school for 4 years with 2 weeks off in Dec. each year. It can be done if you are committed 24/7/350. Double Major, probably not.

In short, no.

You can't double major in engineering + anything else and finish in four years. Less than 50% of students in STEM fields finish their undergraduate degree within 5 years. A very good student can manage an engineering major plus a minor in 4 years.

Which do you plan to do, go to rehersal, learn your lines, or do your homeworks and labs? I'm an engineer and my daughter was in many plays, got close to majoring in theatre in college. Major time commitment for the theatre. Engineering takes a commitment of a mean average of 70 hours per week for success, regardless of which branch, how smart you are, how smart your relatives think you are, how young you were when you built your first race car, how you welded when you were 7....don't matter. Need to put in the time and effort to learn all of that engineering. This combination seems like an impossible combination for a person with 24 hour days, 7 in a week. I strongly encourage you to rethink this folly before you have spent a bundle and realize you are in over your head.

Yeah sure, just hum a few bars and fake it.

But seriously, it's possible if you really want to (though many engineering programs are 5 years where I live).