Do they display that nag screen when you next visit a youtube page once "Continue to Video" has been clicked?
Hopefully, the user gets some sort of warning that their browser is unsupported every time they visit. I suspect even the most complacent of users will want to upgrade if the nag screen is still in their face.
I'm fairly certain that for most IE6 users, the reason isn't complacency (or even ignorance). It's lack of control - corporate environments with "business-critical" ActiveX controls (yes, really), kiosks and so forth.
Hopefully, the user gets some sort of warning that their browser is unsupported every time they visit. I suspect even the most complacent of users will want to upgrade if the nag screen is still in their face.