When Using Sign Language While Drunk Does Your Fingers Slur Their Words?

Yes.
I sign and have found that, like most things, it’s harder if I’ve had a drink. This isn’t really surprising as alcohol dulls your reactions and slows down your motor-neurone system. I’m sure that you’ll have found normal things like sitting up straight, walking, etc harder when drunk. Signing’s not really any different.

Hope I’ve helped!