Yes FedEx does run on Saturdays.
FedEx does deliver on Saturdays just like USPS and UPS also delivers on Saturdays.
If you're expecting a package through FedEx or USPS or UPS and it's expected to be delivered on Saturday then you should get the package.
If not then you would get the package likely on the following Monday.
Still though the FedEx, USPS and UPS sorting facilities and trucking are all running on Saturday as well as Sunday so that the packages get through their system and are delivered to you.