I am looking at am application where there is a companion USB MCU.
If a device is bus powered, it is not supposed to draw more than 100mA until the USB host gives it permission. At that point, it can draw 500mA (at 5V).
I think that if the core supply is disabled, this should be possible. The local USB MCU would control the power enable and DSP reset.
The simpliest implementation would still have the 3.3V I/O supply connected while the core was disabled and reset was asserted. After USB enumeration, the core would be turned on and then reset would be deasserted.
In my experience, SHARCs are OK (obviously not functional) when the core supply is off. We have seen this condition if a buck regulator is shorted.