Is it possible to power the USB Isolator with a linear power supply instead of the PC USB +5V bus?

This would be possible if you use an external adapter cable which does split the supply.

But please note:
Internal voltages are generated by linear regulators. The isolated side is supplied by our own proprietary and very careful designed DC/DC converter followed by linear regulators.
The isolated USB output voltage is generated by the Analog Devices ADP125 linear regulator.
Because of the isolation barrier, this is really always the same low noise independent from host/computer cable type.