Center stance

I have always coached my centers to put their non-snapping hand down to keep them firing off low. I know that a lot of zone/shotgun teams have the centers put their off hand up. We are not a zone or shotgun team and I have a smaller, quicker center this year who has a problem of actually firing off with his head down at times. I am thinking about trying him in a stance with his off hand up to help with this and to help with blocking back for counter, trap, etc. My question is does anyone else teach this and what do you see as advantages/disadvantages.