I'm helping a friend with a Verbatim wireless keyboard/mouse set. He lost the receiver dongle, and ordered (or was sent by RMA-can't remember) another Verbatim mouse with Nano receiver. When he ...

Logitech's, at least, do not. I can't speak to Microsoft's, but they've never had interoperability between different form-factor receivers before, so I'd be surprised if that has changed.