no, it's bad idea. first of all, takes way too much time to implement which would be better put into the single player. second, like others said, they would have to separate the whole thing basically into a game of it's own because the single player having stuff like 100% reflect damage, 100% resist magic and alot of other imbalances or mods preventing you from having the same stuff and classes.
Here's my take on TES multiplayer. First of all, it doesn't have to take time or resources because it can be done by a separate team. That's the route a LOT of developers are taking these days. One team works on the single player and one team works on the multiplayer. Obviously for Skyrim that is not the case, so this is more of a future type idea. Second, I can't stand people who have their mind completely shut off to ANY multiplayer possibilities in TES. These people are, to put it bluntly, [censored]. I can understand closing your mind entirely to MMO or Co-Op or anything else than involves MIXING Single Player and Multiplayer. Those 2 things are, in my opinion, COMPLETELY out of place and stupid and would definitely take too much to do right.
However, and I was right on that boat with everyone else for Oblivion, an Arena-only multiplayer could be awesome. It would be a nice way for TES to go online without perverting the Single Player. And here's how I would do it personally:
Multiplayer, like Splinter Cell or Assassin's Creed or whatever, would be an entirely separate entity from Single Player. As mentioned before, it would be developed by a separate team and everything. What happens is you go into multiplayer, and you create a new character FOR multiplayer. You choose the race, and basically go through the single player character creation. The way it would work would be similar to Daggerfall. Since your character will not grow levels and such, the development would have to be very deep. So there'd be a slew of multiplayer-only advantages and disadvantages to add to your player. You'd have a certain number of points to add to your character. Adding disadvantages would give you some of those points back. This is what would cause balance. After that, you go into the next phase. Skill Development. You would have a certain number of points to put into accessories. Are you a warrior? Put points into powerful armor and weapons. Are you a mage? Buy some spells. Are you an assassin? Buy some stat boosts for acrobatics, buy some poisons.
Basically a mage could pick a spell, perhaps even combine spell effects, etc... much like the single player spell crafting. However, instead of spells costing money based on power, they'd cost points. So you could have a large arsenal of average spells, or you could have one powerful spell, but in doing so you'd have no other options.
You could also set it so the amount of points something costs is based on your specialization, so you can't get this beefed up warrior with a Combat specialization, and then sneak a really powerful poison or enchantment onto your sword because poison's would be too expensive for a Combat class to add; they'd have to settle with a weaker poison that fits their points budget. But someone with a stealth specialization would be able to buy poisons for less points. This would help accentuate the different character types, and you wouldn't see warriors running around with fireball staves.
Now after you've gone through the deep multiplayer character creation, you would then search through gametypes I guess, though I think deathmatch and team deathmatch would be all that's required for a game like TES. I would hate to see TES become a multiplayer-centric game. This isn't a game that would have leaderboards and ranks and level ups and [censored]. It's not gonna have CTF and objective modes and huge maps or anything. Instead I think it would be fitting to keep it to DM and TDM and maybe some Players vs Monsters, and there would be several maps. The maps would all be decent sized with obstacles and hazards maybe (lava pits? etc...) and places to hide, but not too big or winding. They could have different locales, like Morrowind, etc... to really show off the Elder Scrolls universe.
Now in a future game with good combat and an even better engine (maybe Skyrim will have good combat, but I'm not holding my breath), a separate team could put something like this into TES. It wouldn't take away from the Single Player, it would only offer TES an even larger audience and new venues for profit, and give it even more replayability and depth.
It'd definitely be cool to run around an imperial castle trying to get away from a giant orc knight, and using the lock spell that you put points into to close and lock a door to keep that knight occupied (being that it's multiplayer and not all characters would be able to pick the lock, it'd either have to be a TIMED lock spell, there'd have to be alternate routes, or you'd have to be able to bust doors open with your weapon). It could be REALLY interesting and fun, and the depth and variety of TES offers multiplayer possibilities that don't exist anywhere else, even just on what we've already seen from DaggerFall, Morrowind and Oblivion (Climbing Walls, Levitation, Poison, Paralysis, etc...). I really wish so many die-hard SP fans wouldn't be so closed off to the idea. I know they're worried about Single Player, but there really is a way it could be done without taking away from that, and, if done correctly, it could be enjoyable for a large number of people.
And yes, to answer the inevitable question, I've put a LOT of thought into this.