Some games require an active internet connection but it is not due to Steam, it's part of the game itself. When you're off line, I'm not sure what you mean by Steam having to be on. Anyway, I can say that Morrowind doesn't require any active connections as far as I know since I've played it under all sorts of conditions including off-line.
edit: I understand that Steam can seem intrusive and can be an extra layer that may not be desirable and that you may want to do without it. However, they often have really good sales and provide disk-free play. I personally have not found them to be a problem and welcome the chance to buy games like MW , Oblivion, or Witcher for under $10 on sale and get rid of the need to have a disk in my drive. I think some people worry too much about it.
What I mean is, you have to have Steam on to play games. While Steam can be set to "offline" mode, Steam still has to be on. I can't speak for Morrowind, but if I want to play Civ V, and I don't have Steam on, As soon as I double click my Civ V Icon, Steam comes on, and then Civ V loads. From what I am told all Steam games do this. Even if Steam is off, it will come on in order for your game to play. I just assumed it was for Steam Morrowind as well.
Thing about Steam is, you have to be "online" before you can set it to "offline". I tried this and I couldn't play my games, because Steam wouldn't go offline and said it needed to be online in order to go offline. Go figure eh? When I tried to put Steam online I couldn't. I ended up uninstalling it, and reinstalling it again. Now I have it offline again. If it wil not go online again, then I will not bother with it anymore. I am not trying to say Steam is bad, but saying you don't need Steam on in order to play games is wrong. For most Steam games, Steam has to be on. Yes it can be set for "offline" mode so you don't need an interente access, but Steam still has to be on.
Again, for Morrowind I don't know, but the games I have played, it had to be on. If I shut Steam down, before the game loaded, the game would not load up and I coudldn't play it.