I served the mission in South Carolina (loved it and the people). While there I never did pick up the accent that others did, but my speech did slow down and I used works like ya'll, mash that button, and other slang words.
When I first got there so many members and investigators would tell me to slow down when I spoke. When I got home my family said there was a very noticeable difference in that I slowed down when I spoke. So from that aspect the south did impact me, but I never did pick up the southern drawl.