It depends on the dog. Some like to hold, some like to bite and release. The ones that bite and release in my opinion are the hard biters. Although some holders do have hard bites, it won't do as much damage as bite and release and it also won't help if they don't shake either.
But as for your question, yes it will help the mouth doing both running and mouth work.
You could work the dogs mouth the first couple weeks of the keep, stop, and just run him, and during those last few weeks of the keep, his mouth will still be just as good or better come show time.
Having a holding dog could be your best bet if he's holding the right spot or it could be his own demise. What I mean by that is they could tire out the hog and then kill him with a good hold. But also if he's not letting go and if it goes the distance and you can't make a handle due to him still having a hold, his chances of surviving will dramatically decrease. Know your dog's weakness and his strength and help him during his keep.
Example 1: let's say I have a bitch who I've seen finish a hog in :30. I also know that she doesn't have a hard bite but she has that drive to finish and she could hold a hog down for as long as she want. Now that I know all this, for her next keep I will work on her mouth throughout the keep to help her keep her holds. She can't over work her mouth because she had no mouth to begin with.
Example 2: if I have a hard biting bitch, I will work her mouth during the off season(before I lock her) once she's lock, I'll stop all mouth work during the keep. This is just to make sure I don't work the mouth out of her. All the exercises she's getting during her keep are enough to keep her mouth stay strong.