It did! It was some impressively cool tech too. At the time, at least in my country, some ISPs would disable your internet access when you didn't pay, but the LAN between subscribers still worked. So obviously nothing worked, except Skype. My theory then was that it would find a path to route around the disconnection by having the Skype client of a different subscriber on the same LAN, that did have internet access, relay your traffic to the rest of the network.
Group chats in Skype though, those were popular. Nothing else had good group chats at the time, but then again, after VK introduced them, everyone I know quickly moved there. I don't know how message delivery worked there, but you could receive messages that were sent while you were offline just fine. Maybe you got them from any one online participant, or maybe the "supernodes" did some sort of store-and-forward thing, or maybe a bit of both.
I think they really tried to merge Skype with Live Messenger, stripping Skype for parts. And maybe those parts weren't the tech as much as the brand, but we don't know how much tech they adopted.