Yes, they do. Although in between they also play a lot, races, curious and search out.... Half cute and half nuisance.
But if a kitten dont does be curious save short moments, dont play much, but almost whole time lies down and or sleeping - this is of course a big alarm-sign.
Good luck!
ps. I saw he got his shots yesterday or so. After shots most kittens are "down the weather" a couple, three days. And thus - sleeping some extra.