I think it depends if you are willing to use your full utility to help the group out i.e. tank/heal when needed. Use CC smartly (bear stun? cyclone?).
If you’re one of those hybrid dps that is just blindly doing dps (which is low as people here pointed out) then no.
I play a holy paladin on one of my characters, and I’ve done ‘dps’ in heroics, but I was stunning mobs, offhealing on overpulls etc. so despite some meter idiot calling me out on my dps the sane people in the group acknowledged that I was still more then pulling my weight in this way. If I had blindly focused dps that would have been another story…
The point is, you need people that know you are this kind of a team player. If you apply to pug groups, people will not know if you are and I can fully understand they will be hesitant to take you. So make friends in groups, ask if you can come along more often with them etc. I’ve seen people take absolutely trash mages and warlocks, but at least they were a class that had potential to be decent or even great.