Would the earth shake? Sure. Do I think the Twitter folk should do it if the opportunity presents itself? Absolutely. Gets them out of the hotseat of having to attach a business model to Twitter, which certainly won't be popular with the users. No matter how they do it.
Should Apple do it? Why not. They have a huge pile of cash that keeps getting bigger. They're saving it for something, they say -- but what could they possibly buy with so much cash? They could turn into a bank, and I'm fairly sure they're going to do that at some point. iPhones will become credit cards. They'll do deals with Visa and MasterCard like the deals they do with AT&T and Verizon. But eventually they will not need them, nor will they need the credit companies. But that's a long way off. And the money they'd spend to buy Twitter wouldn't make much difference to them. And if they do it right, it translates into leverage for them in a new media market, news, and that could end up being hugely profitable. (It's one they clearly expect to be in with the iPad.)
I remember the initial excitement I felt when I saw Ping, that quickly turned to disappointment when it became clear that Apple didn't have the guts to let their users really communicate with each other over their network. So if Apple bought Twitter that would bring them solidly into the world of easy user networking. It would be worth doing if only for that.
If they merged, that would explain some of the awful attempts Twitter has made to seem Apple-like. In their promotional materials and in the way they screw their ecosystem. Apple does both both with flair and panache. Twitter is a poor imitation of Apple, in every way.
Another reason Apple would like it is because it's inevitable that Twitter will turn the screws on the news business, and Apple loves to get into position where they own the mortgage on a media industry. Look at how well they've been doing with music, and the inroads they've made into movies and television. Now they have entre into news. A deal you can't refuse.