No - toothpaste is in part an abrasive. If it's wetter, the abrasive is less effective at removing biofilm/plaque, and the chemical components are diluted in situ. Your mouth is plenty wet enough as-is.
My experience is that working in an office is _much_ worse for distraction. Even if you're lucky enough not to be in open plan, the shoulder taps and quick chats easily demolish any chance of focus for me. At home I can knuckle down for a few hours and deal with something complex easily.