Most Helpful Guy
He is being honest with you. The worst you could do is not trust his honesty. I get depression sometimes and I don't want to chat or see people when I'm in that mood. Just give him space but let him know that you're still there and you're not going anywhere no matter how long it takes.
Most Helpful Girl
Yes it is very normal. I sometimes don't respond to my phone or messages for days simply because I don't have the energy or motivation. What I find strange in this case is instead of responding to your original message, he texts, "Did you forget about me?" much later. That kind of seems more like he wants you to chase him.
He probably does like you and you could pursue something with him. However you should definitely be aware, that it's going to be very hard for him to be in a healthy romantic relationship until he works on himself a bit first.
The stress of a normal relationship could actually end up making him worse if his original condition isn't treated first. As he grows closer to you, his depression may appear to find when he is actually finding happiness in you. This sounds like it would be a good thing, but it's not.
If you all began fighting or having issues, like most couples do, he could end up taking a swing for the worst back down in the dumps. I say be a supportive friend and encourage him to get help.