They will tell you that they have the right to test it, which they do. The likelihood of them checking is fairly slim I'd imagine. Are you being honest with the state of the charger or is it dingy and you want a new one?
If it's an older magsafe, then they'll likely look at the contacts. If there's evidence of "scorching", then they'll replace it with a new one.
If you have an apple store near you, take it there and they'll swap it on the spot. If they try to charge you, then politely make a stink about it and how you don't want your house to burn down.
I wouldn't expect that they'd have any issue in swapping it, but take a picture of the connector anyway.
EDIT - the charring/scorching on the older magsafes is a known issue. Also known is the fraying that occurs at the connector due to a lack of strain relief. Make sure they give you one with the "right angle" connector.