Queensryche sold something like 15,000 copies of their first indie release on the strength of some good press and radio play before they'd ever played a single note onstage. Again though, that's definitely an exception to the rule. Bear in mind, when you hear an indie release that grabs your attention, even if the artist in question never did any gigging, the road to making it happen probably wasn't "easy." It takes years of hard work to make an "overnight success" more often than not.
As far as trying to "do it all online," here's a good example from my own situation: I'm in what would SEEM an ideal position to do that. I'm doing progressive hard rock stuff that's right up the typical Rush or Yes fan's alley. Between the various message boards I visit, I have exposure to at least 10,000 Rush fans alone. One of the Rush sites has even graciously put up a banner for me at the top of the board, which really blew me away. But in the first week of its release, how many copies has my CD sold online? FIVE. Yep, FIVE. I once read that the average indie artist sells less than 5 CDs from their personal website per year, so I guess I'm doing better than average, LOL. The people who have bought a copy love the heck out of it, but getting folks to actually take that step and order a CD is like rolling a boulder uphill. MAN, it's hard.
Of course it's possible that things will gain momentum once more and more folks get a copy and start discussing it on the boards, and who knows...perhaps over the course of the next several months the disc WOULD reach my sales goal (at least 500 copies but preferably closer to 1,000) without me playing live shows. But I don't plan to sit around and wait to find out. A marketing course I once went through maintained that "most independent artists will realize 90% of their album sales at their live shows," and I think for most that's probably true. So, despite my general distaste for the whole "club environment," I'm gonna head out there.
Anyway, to revisit the original question, is it possible to have a smash success without playing live? Yes...unless you're doing something that isn't "trendy" and you aren't a guerilla marketing genius and don't have connections at major radio stations...in that case, ya better figure on getting out there and playing live if you don't want to have boxes of CDs collecting dust in your closet. ;-)