Speaking from some degree of experience, I can say that boots easily collect moisture on the inside during daily wear on a hunt. The right socks help, but eventually the boot material gains moisture. Whether it dries or not is a function of many things like humidity, air temp, external moisture, and efforts to dry them out. A Gore-Tex liner helps keep feet dry and helps exclude external moisture from the foot, but it does nothing to keep the outer boot dry. You can have waterlogged boots and still your feet don't get soaked.
As Ron pointed out, correctly treating the leather is key to moisture exclusion. Don't forget to seal those seams with a dedicated product, because greases won't reliably stop moisture from getting past needle holes and mated seams. I haven't found anything which will keep leather fully dry in constant wetness and high humidity. That's where additional steps come in, like changing socks, liners, stuffing with newspaper, additional heat.
Newspaper is an old reliable trick for absorbing moisture. Someone needs to invent a super-absorbent boot stuffing which does the same thing. Stuff them in your damp boots tonight, pull out and hang in the morning...boots are dry inside.