Having engine running on the 'booster' vehicle is not a problem for
short term; it
can (potentially) be a problem for the Regulator if left for an extended period of time however;
It has nothing to do with amps - it is simply because the car/truck alternator operates at a higher voltage than the motorcycle regulator - typically over 15+V vs 14+V on the bike;
so what happens is the Bike Regulator 'thinks' (sic) that there is too much voltage so needs to shunt more current through the regulator shunts in its seemingly logical attempt to reduce the 'system' voltage; now since nothing the bike regulator attempts to do has any bearing on the voltage the bike system is seeing (i.e. the running truck voltage) it actually goes into full shunt mode where ALL of the current being generated by the stator, is being expended ONLY within the regulator and none actually going onto the system. Indeed it is also going to be sinking current from the booster vehicle through that regulator. Over an extended period this means the R/R will continue to get hotter and hotter and eventually self-destruct (especially if an SCR R/R which already run MUCH hotter - the R3 uses a MOSFET R/R which is more efficient but it's not a healthy situation)
So I would say
1) It is actually 'OK' to have booster vehicle running - however it should be disconnected (or booster vehicle engine killed at the least) once the bike has started.
2) It really should not be necessary however to start the booster vehicle - starting requires current capability the discharged battery does not have - a big car battery should NOT require to be further backed up by an alternator in order to provide the necessary shortfall. But note also that you don't want to leave the booster connected with ONLY the BIKE running, as now that is also trying to charge THAT battery. (If it won't run in this condition without having to have the booster still connected to maintain running, accept the fact that your bike battery is toast)
3) Again, this potential R/R failure is not a sudden death - it will require running for a prolonged period before the R/R bites the dust (and not even to say it will absolutely happen - but you sure are cranking the risk factor to keep it connected)
In summary you really shouldn't need it running - so better safe than sorry and just leave it off.
But if you feel you have to, then once started disconnect it and at the bike end first.
Some other tips:
Use REALLY heavy-duty cables with strong clips with very high spring tension to minimize any resistance between the booster battery and the boost-ed one
DO not connect and immediately attempt to start - it's going to be more productive to just leave it connected for a bit - the boost-er WILL provide some charge into the problem battery and even if not enough to start alone, it will still help the situation. Even a few minutes will be beneficial, but longer is of course better.
Other tidbits
The urban legend of causing ECU fails etc with booster engine-running is just that - file that one along with the ECU fails for shutting off with Kill switch - no substance in either of those whatsoever. (thinks to himself - oh dear what have I just opened up withe Kill switch argument
)
Could cause Stator failure? No - a stator ALWAYS runs flat out utilizing a shunt regulator so there is no difference to the load on that; max is max, it cannot produce any more
Bike susceptible to 'receiving' higher current due to the capacity of the truck plus alternator will damage 'other stuff'? No - you cannot 'push' current - current is a factor of the load and the voltage supplied to it - the load is not changing therefor there is no* extra current that will be consumed by the bike
* OK - technically there WILL be a slightly higher current simply because the system voltage is now higher, but that is not significant. Think about it - you already have a battery constantly connected to your bike that is capable of supplying 200+ Amps - some 300! Does that mean that your battery is attempting to force all of that into your bike? Of course not - so in that regard the running vehicle is no different. (but again, understand the
Voltage impact on the bike regulator)