Except that without N bonded to E and L E fault will not cause any fault current to flow (think about it there is no circuit...) but will raise the N way above E, probably up to the full generator output voltage. Bear in mind that most switches and MCBs are single pole in L then things "switched off" aren't. Also as N and E are quite likely to be interconnected somewhere the installations E could also rise to the full generator output voltage.
One end of the generators winding needs to be bonded to the frame of the generator and to local earth and to the main earth terminal of the installation. It is the bonding of local earth to the main earth terminal and thus the suppliers earth that can be problematical with some types of installation.
Assuming that the gennys earth terminal also bonds to one of the generators phases.