Unless you have an unlimited developer budget (and who does?) spending time and money on IE support is also user-hostile. It's just hostile toward a different set of users.
That money could be spent on improving the user experience for people with good browsers, developing new services, lowering prices, or any number of other things that would directly benefit the 90% of your users who have actually entered the 21st Century.
An IE6 boycott would be user-hostile in the same way that the SOPA blackout was user-hostile.
In the SOPA blackout, millions of innocent people were intentionally blocked from all those sites for 24 hours. Their convenience was sacrificed in order to apply pressure to people who actually were in a position to make a change.
The purpose of an IE6 boycott will be very similar. The purpose is not to hurt innocent workers who have no control over their computer, but to apply pressure to managers who actually are in a position to change things for the better. Even if the only change they make is to allow employees to install Chrome Frame.
The purpose of SOPA was to call attention to a bill that had enormous implications for the world at large.
The purpose of deliberately breaking IE6 support would be. . . what? To tell customers that we don't like old clunky technology? Seems just a teense less noble, don't you think? Especially in response to a situation that the free market can easily handle unmolested.
If you want to not have to worry about IE6 anymore, all you have to do is stop worrying about IE6. You don't need my help to do it. Though, if the only thing stopping you is fears about alienating customers I'd certainly be glad to help there - just send 'em my way. Can't say I even know how to support IE6 anymore, but if they've been able to cling to it this long I imagine there's a good chance their money's green enough to make it worth my time to re-learn.
Anyway, I'm against anything that's intentionally user-hostile as a matter of principle.