Green or white tea, yes. Blends that are greater than 50% green or white, I would count half the amount towards water. Caffeine free herbal, yes most of the time. Depends on what is in them. Black teas with caffeine, no.
But that is just me.
I typically drink four to eight 8 oz. cups of tea per day, usually half green tea, half oolong or earl grey. I have some other assorted black in my drawer, but I haven't been in the mood for them lately.
I even count black tea with caffeine. The amount of water you're getting from it is MUCH more than the amount of extra water loss due to the caffeine, so I just count it all because I don't really care if I'm an ounce or two off for the day.