Sure it can. Although if you are feeling OK MOST of the time, maybe it is delayed "baby blues" rather than full blown depression. I had the same thing, and mine started about 5 weeks postpartum. Little things would make me cry like a baby! :)
I think the delay for me had something to do with the fact that when you first get home, you are so busy getting acclimated to having the baby and trying to figure out how he or she is going to be, feeding baby, when baby sleeps, going to doctor, etc., that you don't have time to stop and relax. I found myself getting very tense and anxious after a few weeks. My husband helped a lot, he would take the baby on the weekend between feedings and I would sleep, he made sure I was eating, all that good stuff! :) Also, try to take some time out of the day for you! I know it sounds crazy, but you don't even have to go anywhere. Just take a shower by yourself, or a 30min nap. It did wonders for my mind!
**Most importantly, talk to your doctor. Ask for help if and when you need it. No one can do everything on their own!! Good luck and enjoy your new kiddo!