Both our boys were crated when they were puppies, but they were only shut in it overnight and then that was more to prevent destruction and 'toilet accidents'. The door was left open the rest of the day and it was their choice if they went in there for a snooze or not.
Our vet told us that a puppy's bladder doesn't really reach full size until it's the best part of a year old, so you have to expect a fair share of accidents in the house - all you can really do when they're very young is to do everything you can to encourage them to have a pee outside last thing before they go to bed. Eventually they learn to hold a wee overnight, at which point we stopped using the crate.
Even now, at four years old, if ours are particularly desperate they'll whine and because the proverbial mouse's fart wakes me up, I'll let them out in the back garden.
The odd thing is that at home they sleep downstairs in the hall and in the course of an average week they'll get me up maybe 2-3 days out of 7, but when we go to our static caravan on the Norfolk coast, they sleep on our bedroom floor and not once this year have they got me up overnight. I guess it must be a security thing, in that they know they're close to the pack leaders (me and the missus) ...