If the battery has no bad cell or cells and is not to far down, yes, a good alternator will recharge it but you may have to drive a while depending on how far down it is. If it sets a lot get one of the $39.95 Battery Tenders fromNAPA or any other parts store and connect them when it is setting. I have used them for many years and have never had a dead or low battery as they will kick on and keep it at peak charge and also just to move the electrolite from time to time.
Ron
