Yes, the sleepy baby term generally goes with newborns but the term can also be used with some babies who sleep too much & not gain well up for a few months, too. Again, the "output" in wet/poopie diapers is important. Normally, if baby is gaining well and is also sleepy, then baby should be woken up about every 1 1/2 to 2 hours. It all depends on that output and being a "healthy, happy, growing baby," as you mentioned.
During the first few months, especially, if there are any concerns, seeing the ped can be positive.