Sure, many people make their living as just PCB designers, and I have even done that myself.
The trick is having a few key clients who trust you and can give you regular work.
If you are out of clients and have to scout around for just layout work, it may not be easy.
But it's a different world now with the likes of freelance etc.
Often you can value-add, like doing BOM's, sorting manufacture, designing test jigs etc.