Interesting--I dug out my set of wiring diagrams, and, according to them, the horns are connected directly to the battery thru the TR4, but the horn current is in the ammeter in the TR4A. In no case does it depend on whether the generator is running.
I measured the horn resistance when I did my MG, and as I remember, it was about 1 ohm. So, unless the inductance was significant, the total for the two horns, assuming a 50% duty cycle, was about 12 amps. I don't think that would be a problem for the ammeter.
As for me, I much prefer having an ammeter over a voltmeter. The ammeter tells me immediately if the battery is discharging or charging. The horn and starter loads are large but brief, and it doesn't matter much if it doesn't include them.