Oh, you mean that tennis ball in the back of the mouth thing? Yeah, you'll have that. It really does sound like you're drunk when you're talking. Dry mouth sometimes goes along with it. Taking care of the anxiety takes care of that symptom pretty much, although I still have it every now and then when I'm in a REALLY STRESSFUL situation.
Know who Stephen King is? The guy who writes the scary stories? He has panic disorder. (Go figure). Anyway, when he was a new author his agent got him an interview with an editor where King was presenting his manuscript. The editor liked it a lot and was attempting to charm Steve with a lot of freindly chit-chat. Poor Steve was terrified, and got that dry mouth can't talk response. All he could do, finally, was get up and squeak, "Me go now," to the editor and high tail it outta there.
Ever since I read this story (which King tells about himself) I have used "me go now," whenever I need to leave a conversation or just as a fun way of saying "OK, you win," to someone.
This too, shall pass.
The short answer is: YES
The longer version is: Sometimes I would stumble over words, my speaking voice would become more staccato, I'd constantly mispronounce words... It definitely can be part of anxiety and/or essential tremor. All of which have vastly improved for me since I started medication.