Well, your tamagotchi -will- get lonely if it doesn't have any friends, but I think that depends on the kind it is. My Masktchi is doing fine without any friends, but my Hanatchi got depressed easily cause she didn't have friends to connect with. At least, I think...
I wouldn't recommend not connecting it though. Let it have friends, if possible. Maybe then you can have it for many generations! (BTW, my Hanatchi died, and it was only first generation, so don't let it happen to you!)