Unfortunately, no. 

Plugable BT-KEY3 and BT-KEY3XL are Bluetooth 3.0 devices and don't support inter-device switching simply with a button press as some newer keyboard models might. The Fn + Q/W/E keys change the behavior of the keys to accommodate each operating system, but it doesn’t switch between devices. 

For example, Fn + W enables the F1-F12 keys in Windows, while pressing Fn + E enables them to control playback functions in iOS. Like many Bluetooth keyboards, this keyboard can only be connected to one host device at a time and is connected and disconnected in the Bluetooth settings of the device it is connected to.