A donor bike with a battery that dodgy simply should not be used as a donor. A car battery so weak that it cant boost a tiddly bike battery is unlikely to get the car out of the garage in the first place.
The risks of running the donor are:
- Over charging the weak (rescued) battery, but in the short time its connected not much harm will be done. Anyway the donor charging circuit is voltage controlled so overcharging is unlikely.
- The rescued starter will send voltage spikes and noise into the donor electrical system. During a normal engine start, sensitive stuff is switched out. But in this case, all that sensitive stuff is lined up to get fried. Even leaving the ignition on risks smoking the stereo and maybe the body ECU.
- connecting jump leads to an internally shorted battery can cause enough current surge to damage the donor alternator.
A flat car/bike battery so bad that it's sucking all the charge from the donor would indicate an internal short circuit. If it can be got to run at all, the alternator could be overloaded trying to feed a short circuit.
If the donor engine is switched off and connecting that last jump cable clamp causes some serious arcing, its likely the failed battery has shorted out internally. Trying to add more power by running the donor engine risks blowing at least its alternator and potentially a lot more.
So however its counted dont run the donor engine. The risks are too great and the benefits (if any) are minimal.