Yes, no, and Maybe...
... if, and only if, both of the devices ship with a Unified receiver you can program one of the receivers to communicate with both devices. You would need to download the appropriate utility software from Logitech's website. Until you reprogram one of the recievers you will need to connect both. If either or both devices use a plain receiver you will have to connect both receivers. Only the Unifying receivers support multiple devices.