With having to send my Samsung "24 BX2440 monitor in for repair/replacement, I was wondering if they would let me upgrade to a 27" if I paid the extra $?

Has anyone here done this before with a monitor or other component?

I doubt it. Most warranty repair or replace options only allow for replacement with something equivalent to the item that failed. You might get a nice employee who would do what you are proposing, but it would be an exception and a rare one at that. It would come down to how well you plead your case and how insterested Samsung are in keeping you as a happy customer.

It doesn't cost anything to ask but don't expect anything. It would be a rarity for this upgrade to be granted and i suspect that you would need a good 'story' and a sympathetic rep.
-- you might also search their web site. What about the etailer? Will they take it back and allow you to upgrade? Then they can do the exchange with Samsung

Asking won't hurt.. they won't bite!