I think thats a case-by-case type answer...as I understand it now the lcd/glass are pretty much on top of each other so if the glass is damaged, chances are the lcd is too. Apple will replace for $199 I think
please chime in if I'm wrong
edit: sorry about your misfortune by the way...or clumsiness
Agreed. The way I see it, it doesn't hurt anything to ask. Don't be a jerk and if they won't budge, call it a day. Heck I've heard people even getting them replaced over the phone.
This is assuming you have an iPhone 4. They aren't so friendly with older models.