You can achive the required power loss by: 1) pulling the dongle out, 2) using a USB hub with simple toggle switches (or a KVM Switch), 3) putting the computer into hibernation, after which the dongle loses power (you can't have the dongle on a permanently powered USB hub for this to work, also just sleep might be enough if you set your computer to cut the power to the dongle during sleep). The thing is to understand that the pairing is (temporarily) lost as soon as power is lost for the small Logitech Unifying dongle.
TrayTip Could not open the Unifying connection program,`nīasically that code is only opening the Unifying connection program, but speeds things up. As soon as you have re-paired, you can switch on (or re-insert or wake the computer with) the Unifying dongle to put it back into operation (it then waits for a missing pairing) TrayTip Re-pairing Logitech,To disconnect: pull dongle, hibernate or use a USB switch to disconnect the dongle Run, C:\Program Files\Common Files\Logishrd\Unifying\DJCUHost.exe this is the Unifying connection program This solution requires some seconds for re-pairing each time, but is fast enough to be a useful method. I solved this, to some extent, with AutoHotkey and figuring out what causes the de-pairing. None of the Unify devices appear able to do this. The only Logitech device that can do this is the new K760 keyboard for bluetooth. You'd also need to have the input device store the state (caps lock, num lock.) it was in for each transceiver. If you added the ability to have the input devices (mouse, keyboard.) pair to multiple transceivers, you would require some sort of additional buttons on the device to switch between them. Sit, if you see a signal with the correct encryption and ID, accept input, otherwise ignore. That's because the transceiver only has to sit there and accept a signal it recognizes, otherwise it is passive. The problem is that the transceiver may have the ability to recognize something like 5 devices, but the input devices can only recognize and pair to one transceiver. I suspect the answer is that when you pair, the transceiver and the device exchange several bytes of random data and form a key to both allows the devices to recognize each other and to encrypt their wireless transmission.
There appear to be similar questions on Logitech's site so you can search there as well.
I'm going to answer no - it is not possible.