This is actually the same thing.

Your brain processes language differently when “doing a funny voice”. After trauma to the brain such as a stroke, the usual pathways for language processing can get blocked. The brain finds a work-around by sending your speech via the funny-voice neurones.

Weird, but it can keep you talking after brain injury.

I was just wondering if this was related. I was sitting at my neighborhood bar in Kentucky listening to a British couple have a conversation next to me. I was very drunk. Eventually I started talking to them and instead of my usual voice, everything came out British. I don't remember everything that was said, but they were convinced I was also British. Eventually I tried to give up the act but I couldn't find my normal voice. It actually freaked me out a bit because I was legit not trying to do the accent anymore but everything I said just kept coming out that way. They didn't think I was an asshole and had a good laugh about it.