Unifying definitely lets you pair multiple devices (keyboard, mice) to the same dongle, but I'm less sure about whether it lets you pair multiple dongles to the same device(s) and then hot switch between them.
You can pair a single device to multiple receivers and the "switch" button on each device will let you cycle between each receiver. I use the same keyboard and mouse with both my personal computer and my work computer. Every time I need to switch, I just need to use the device switch button on the keyboard and the mouse.
Logitech also makes or made keyboards with 1-2-3 hot swap keys that allowed quick switching with a single press.