Unlikely, but possible. Please see the proposal for single phase operation of three phase generator from one manufacturer in post#77.
The generator is rated for full load capacity with its cooling fan running. So its cooling capacity may not be sufficient to meet about 15% over load on one phase. It is helpful if you quote some standard on this issue. Some standard says only 105% phase overload........
Even if you follow that 105% trip standard of yours, the OC protection relays are fed with 1.0 pu that the CTs pickup on the generator lines.
As I said, don't you just believe me, try it. If you spread out the winding in a plane, you must see that there are areas in the generator, loaded as discussed, to be very cool as those coil slots don't get hot. Remember that the other two coil groups are loaded with 1/3 of their respective currents. With a rotor in between, it isn't hard to understand that the cooling air swirls around the coil slots as it pass from one coil end to the other. The extra heat caused by one coil group with 115% overcurrent you are concerned about is compensated with the large volume of cold iron in the stator.