TN system for generator

Is it solely related to some value that will ensure RCD protection will operate?

I don't think so. For conventional L-PE faults it has no baring on the matter (as being a TN system the earth fault loop doesn't include the electrode). For faults to true earth (either directly or via a shock victim) the loop impedance is full of unknowns - the resistance of the soil around the fault/victim (likely to be significant - possibly several kΩ) and in the case of shock the body resistance of the victim as well (usually in the 1kΩ ballpark). Additional protection by 30mA RCD should remain effective in any event - if the loop impedance is too high to trip the RCD the current flow will be so small as to have a minimal shock risk - in a way the situation almost degrades to a separated circuit.

The 20Ω figure for source electrodes comes from BS 7430 I believe, but seems entirely arbitrary - it's the same for a huge system supplying a city block as for a little standalone generator - there's no apparent relationship to the size of the supply, extent of the system supplied or or type of protective device.

There is one situation where the source electrode value does become significant and that's when your TN system has a TT branch from it (like a TT'd outbuilding from a TN main building with a generator backup) - as it'll directly affect the TT systems loop impedances, and could be a significant problem where higher rated RCDs are used (fault currents could be too low to trip RCDs but still be high enough to be a shock hazard). But as long as you're sure your system won't be feeding a TT'd section, it's not a worry.

   - Andy.

My question was really about the first “T” in TN-S, specifically relating to a typical stand alone three-phase generator such as might be used at a festival or other similar event in an open field. 
For example, does hammering an electrode into the ground and connecting it to the gen set earth terminal (neutral and earth terminal are connected on gen-set start-up) establish the “T” regardless of the electrode resistance (Re)? Or, as I suggested, must it also be reasonably confirmed that the protective device on the gen set will operate on a first fault to true earth, say along the cable feeding the distribution units? That being the case, then it is likely that only a RCD or similar device will be suitable.

I understand that the first fault to true earth will also have a resistance but how can that be factored in other than to keep Re as low as possible. 
So when does TN-S become IN-S? 

must it also be reasonably confirmed that the protective device on the gen set will operate on a first fault to true earth, say along the cable feeding the distribution units

I don't think that's possible (because of the lack of control of the loop impedance) nor necessary - unless additional protection is required. Normally double/reinforced insulation (i.e. sheathed cables, suitable for the conditions) suffice.

So when does TN-S become IN-S? 

Comparing with an IT system (for which BS 7671 is similarly bereft of useful numbers or means to calculate them) I'd have guess as Rb being sufficiently high that a any shock current via true earth would be insufficient to cause harm - e.g. 23k Ohms to keep shock currents below 10mA. For lower resistances (and so higher potential shock current) ADS on 1st fault would be needed.

   - Andy.

must it also be reasonably confirmed that the protective device on the gen set will operate on a first fault to true earth, say along the cable feeding the distribution units

I don't think that's possible (because of the lack of control of the loop impedance) nor necessary - unless additional protection is required. Normally double/reinforced insulation (i.e. sheathed cables, suitable for the conditions) suffice.

So when does TN-S become IN-S? 

Comparing with an IT system (for which BS 7671 is similarly bereft of useful numbers or means to calculate them) I'd have guess as Rb being sufficiently high that a any shock current via true earth would be insufficient to cause harm - e.g. 23k Ohms to keep shock currents below 10mA. For lower resistances (and so higher potential shock current) ADS on 1st fault would be needed.

   - Andy.