Mine does for any sick leave longer than 1 day. OTOH, we (staff) don't get a defined number of sickes per year, but rather unlimited sick leave as required.
So there's no saving up of leave, but if you break your hip (to quote a previous poster) and are out for 6 weeks, you're fully covered. And they do - had one person off for over 6 months after a car crash - receiving full pay the whole time. For a company that'll go that far I'm inclined to not abuse the system (well, I wont abuse the system as I might need it one day... hopefully not!)
No payouts on sick leave when you leave either, but I've got no issue with that.