The voltage will overcome the natural insulation of the air inside the driver and burn up the diaphragm. I've seen this way too often on the normal bias sets which were used with transformer boxes. The later SRD boxes used 450V zeners to clamp the output plus the protection in the earcups but it just didn't always work. The phones will continue to work but it is a vicious cycle since the charred remains of the diaphragm shorten the D/S gap so the driver is even more sensitive to arcing so it happens again and again.
For the HE90, Sennheiser clearly states in the specs that they should never see anything in excess of 1000V P-P. That would be double the bias voltage (so 460V P-P for the normal bias Stax sets) but I think the SR-007 can take a bit more than that. They aren't really bothered by 900V bias and the driver construction sure points to that.
On this subject, it is amazing just how messed up ESP drivers can be yet still produce sound. The first Micro-Seiki MS-1 I received produced sound but it was very faint. When I opened them up there wasn't any diaphragm left, just small crumbles scatted all over the driver yet it made sound...
Two things you can do, add a servo with the output running through relays which shuts off if the offset goes too high. The Stax SRM-717/727 and the T2 use this setup with the threshold at around 20V.
Another Stax trick, feed the output through 5k1 resistors to protect the headphones and the listener.
In reality this isn't much of an issue since the distances inside the headphones are so great that insulation breakdown should never be a factor. Stax did ground the SR-Omega chassis just to be sure but I doubt it was ever really needed.