Thanks for posting your question here! No, you cannot use the Plugable 10 Port USB 2.0 Hub for your need. Sorry about that!
As per USB specs, a USB device can only be connected to one upstream host computer at any given instance of time.
The Plugable 10 Port USB 2.0 Hub can only be used to connect multiple USB devices to a single upstream computer. If cannot be used to connect one USB device to different computers.