Depends. If the drama is terribly bad then no. By that, I mean if the characters are all acting retarded and doing the dumbest stuff. That's something that pisses me off and I won't watch a drama that pisses me off. If it's boring, then I'll find myself fast forwarding through most of the episodes. I could try to suffer through it, but If I can't then I just drop it. I tend to not like dropping dramas. I'd like to finish them no matter how horrible they may get, then I can give them a terrible score later, but I hate when I start something and don't finish it.
Still, I like to look up dramas before I start watching them...