Is it feasible to have a Touchscreen with 2 (mirrored) USB outputs?
Use a USB switch. These are purpose designed devices that allow one usb device to be shared among multiple computers. Basically like a KVM. There are dedicated ICs you can use for this. 

Alternatively, run two usb cables. 

But your proposed solution will work okay. All USB hid is is just a response to the host with the position data (the slave does not send data randomly, only in response to a host update request). If your controller can responds to two independent 1 MHz , independent clocked requests set the same time,  it will work fine. Keep in mind that the unused computer may see unwanted user input. 

An easier solution, still not as simple as a USB switch or two cables and manual switching, is use two USB controllers. Easier to implement. Just tie the analog data input into both controllers. They can even have the same exact firmware. Cost wise your looking at 2 simpler microcontrollers instead of 1 powerful complicated one. The time you save coding and testing would be worth the design change.