Skudor is right really; it doesn't stop her from performing the song outright, it just establishes her as an addict. The problem is that it can really kill her ability to do the song. If, for example, she shows up drunk to the recording sessions, David Arnold and whoever is in the band lose an entire day because Winehouse has been in the wine house. That's not to say she won't be able to pull her act together long enough to be able to record it, but she keeps proving she's not making any effort to get clean, and this isn't the first concert she's shown up to while strung out; she did it for the Grammys last year as well.
On this we agree. It has nothing to do with morality or judging her worth as a human being; it has do with whether she is professionally capable of doing what she's being asked to do, without costing her employer excessive amounts of money to do it. That's my main issue with Winehouse, and unfortunately it appears she's not making any progress at this point. That's sad for her, potentially tragic, and as you and others have noted, at least in the short term it does not bode well for her chances of getting this kind of work.
If the recording is already done, and it's good, then the point may be moot, though I really can't see her doing any publicity appearances, being invited to the premiere, etc. But stranger things have happened. Ozzy Osbourne at the queen's silver jubilee party? Wow!