It won't be TT unless there are two separate electrodes - one for the source (generator) and another for the consumer.

The usual arrangement for generators is TN-S with the local electrode serving as the source electrode (like the one that's at the substation in a public supply), or for small systems (e.g. <3kVA) a separated system is sometimes used (neither the source nor exposed parts of the installation deliberately connected to an Earth electrode).

IT is a possibility - especially if someone has connected the installation's exposed-conductive-parts to the electrode without creating a N-PE link. Whether that's the best choice is another matter (IT systems are usually chosen where resilience on first faults is needed - and normally include insulation monitors and warning systems).

   - Andy.

If it really is an IT system, connecting more earth electrodes to PE won't make it another type of earthing system - it will still be insulated from Earth.

Was it really an IT system? It's unusual, especially if PE in the cabin is taken from the generator neutral.

very small portable gensets often do have no NE bond - both ends of the windings come out to the socket but there is no specific sense  of live and neutral. The clue is that the earth to live voltage measures some intermediate thing that is very load dependent.  It does mean that having an RCD at that point is not much use, as those the in and out bound currents are always in balance. 
Such gensets are fine for one or two items and double inusulated power tools, and are sometimes seen throbbing away at the back of mobile burger vans and on small building sites without power etc.  For more permanent installations and when more than a few items are involved, so there is somthing like a CU somewhere, it becomes better to create a clear N-E link, so that ADS and RCDs all work to plan.

An earth rod at genset becomes  desirable at the time that transition is made.
Mike

mapj1 said:

It does mean that having an RCD at that point is not much use,

Second fault, IT system ???

Is only useful if one of the 2 faults is between the genset windings and the RCD, and the other fault is on the load side of the RCD. I'm pretty sure 2 pole  RCD right at the genset when the genset is truly floating is not much use, against any no of faults if they are all on the load side. A similar problem arises with fully floating isolation transformers. It will help if you get a fault between windings and chassis, of course, but there are better ways to detect that.
Mike

mapj1 said:

Is only useful if one of the 2 faults is between the genset windings and the RCD, and the other fault is on the load side of the RCD.

Disagree

1st fault to Earth (downstream of the RCD), nothing happens, but a TN system is formed.

2nd fault to Earth, the RCD will then operate.

2nd fault to Earth, the RCD will then operate.

I'm not seeing how either - if both faults are downstream (to Earth or just exposed-conductive-parts) the two poles at the generator are still in balance.

If all the exposed-conductive-parts are connected together and the two faults are on opposite poles, you might well get ADS - but it'll be though overcurrent protective device (or the generator stalling) rather than RCD.

   - Andy.

but a TN system is formed.

But a TN system with the N-PE link on the wrong side of the RCD....

   - Andy.

This is the case I mean

Mike

Agreed - in this case, with only a single circuit, nothing will happen unless an OCPD operates.

There are times when RCDs need to be backed up by other devices, but this is covered in BS 7671.

mapj1 said:

This is the case I mean

As above, OCPD would need to operate here, where there is just a single circuit ... BS 7671 doesn't really cover anything other than faults of negligible impedance.