Can this be done? I know it can be physically done, but I seem to remember reading somewhere, that it could damage the bike engine gearbox.
I ask because if your car has only broken down, not accident damaged, the recovery services seem to send out a van with a
fold out Dolly, not a flat bed.

AFAIK, you should not do this for long distances, as you don't get oil movement within the gearbox until the engine is running, so you are more likely to get wear of those components that move when you are in neutral and being towed. If you need to be moved with a towing dolly, then lock the front wheels and tow backwards with the rear wheels off the ground.

As above, no recovery service will move your vehicle with the driven wheels on the ground, you shouldn't tow a car with an autobox with the driven wheels on the ground even in neutral, I'm guessing for simillar reasons.

If you feel you need recovery by flat bed, I'm sure it's something that could be sorted, all the recoverys I've seen recently have had the car completely off the ground.

As above, they'll only usually use the dolly to get you out of a dangerous position or to where the car could be more easily loaded onto a flatbed - shouldn't be more than a few hundred yards.