Can you join an agency if you’re not front-facing?

I’ve been considering joining an agency mainly to fill idle time and stay consistently booked. I’ve been working independently for a while and haven’t had any issues operating on my own.

The one thing is… I’m not front-facing. I tend to keep things fairly discreet and prefer maintaining a low public profile.

I’m curious how agencies typically handle that. Is it still possible to work with one without being publicly advertised or heavily promoted?

If anyone has experience with agencies in the LA or OC area that are comfortable working with more discreet arrangements, I’d appreciate any insight.