I only had my kids use a plastic diaper cover over their underwear for naps & bedtime. I did it for a few months because they were pretty young when I PT them (under 1 1/2 yrs old). The issue I would have at have them wearing it full time is what if they went, you'd want to know right away to take them to the potty.
We used the Gerber ones for a little while over undies for outings until he got comfortable using the public toilets. They didn't always keep his pants totally dry but it was much better than if he had an accident without them on. I think I'm about to try them for naps... Good luck!
Re: Plastic training pants?