I can speak of my own experience. Years ago I subbed for a friend on a couple of dates for Into The Woods on double bass. We both played un-amplified, and I ended up feeling like I was playing more for the band rather than the audience or cast. The venue was an old repurposed movie theater, and I felt like I wasn't cutting through the mix.
On the other hand, I recently played a production of a new show, Spring Awakening, where I doubled on bass guitar and double bass.
My setup was:
Fender P > SansAmp > direct to FOH and a line out to a small combo I kept on stage for monitoring.
Double bass w/Realist > Fishman Pro-Platinum > FOH, and they put a monitor in front of me.
After some dialogue with the sound man to get the monitor level right, this worked perfectly for me. That score is a challenge for the double bass; some songs call for a strong, rock-style bassline to support the entire band, some songs have you blending with a string quartet, and some songs go back and forth between both. I don't know if the theater you're working in has the capabilities to do something like this, but it really worked for me.