Quick Answer:

The Y-mouse is only capable of accepting data from one device at a time. As long as it is accepting input from one device the other device will not be able to send data through the Y-mouse.

Further Reading:

Y-mouse Standard Behavior:

Our Y-mouse devices are designed to only accept data from one attached device at a time. This means that any additionally attached devices will be ignored by the Y-mouse until the first device stops reporting.

Or-ing Y-mouse:

The Or-ing version of our Y-mouse devices are designed to accept data from two devices simultaneously. In the case of using two mice simultaneously, the Y-mouse's output will be an average of the data coming into the Y-mouse from the attached devices.