My late uncle came from the same background (Germans from Russia, rural North Dakota) as Lawrence Welk. They were the same age, give or take a year. Yet my uncle had no accent such as Welk retained all his life. As has been said, I think it's what you want to sound like to a great extent.
I've also noticed that G.W. Bush, when he's giving a campaign speech or trying to be down-to-earth, drops his g's. When he's giving a serious speach, he doesn't. And he likely isn't even aware of this.
Cum catapultae proscriptae erunt tum soli proscript catapultas habebunt.