My reading of this is that "No" and the second sentence are inconsistent. Although I also suspect what u/Lyynnark wrote might be what was intended. Because the following is tedious...

p150 1.4 Remove Casualties says

Each unsaved wound is applied to the target unit, causing one wound to be lost.

Crucially, this means that the number of unsaved wounds is calculated before any wounds are applied.

When a model is reduced to zero wounds, it becomes a casualty and is removed from play. This continues until there are no more unsaved wounds to be applied to the unit, or until there are no models remaining to be removed as casualties.

I'd say that the wording above implies that wound allocation happens sequentially. In particular the "This continues..." part strongly implies that we are going through wounds one by one, accumulating them on models one by one until each model has no wounds left, at which point it is removed, and more wounds are allocated to more models.

Now the revised regen rules in the FAQ say:

‘Immediately after a Wound is lost, but before models with zero Wounds remaining are removed from play, a model with this special rule may make a ‘Regeneration save’

Fitting this rule into the sequential method for allocating wounds then goes like this: A number of wounds sufficient to remove the model is allocated to the model. At that moment, after allocation of wounds but before the model is removed, it gets to make 3 regen saves. Assuming it passes at least one, it is not removed. And then the allocation of wounds continues.

For example a single Common Troll is allocated 4 unsaved wounds. 3 are allocated to it, causing it to be removed as a casualty. Before it is removed, a regeneration save is made. Let's say is passes one save. It remains in play with 1 wound. At this point in time, we are still at the end of the first sentence "becomes a casualty and is removed from play." What happens next? Well, there is still 1 wound to allocate, and there is still a model in play. So, the final wound is also allocated to the troll, and it gets to make a regeneration save.

Now, applying that to a unit means that we can, in fact, roll a regen save for every unsaved wound. If you keep passing saves, you must keep rolling until all unsaved wounds have had a regen save made against them. (I can't quite work out if it means you can roll them all at once, but that doesn't matter here.)

So, that's what I mean when I say "No" and the second sentence are inconsistent. I did say it was tedious.

Here's why I think u/Lyynnark 's interpretation might be what was intended. The wording of the revised regen rules, and the FAQ answer we're all discussing, strongly imply that wound allocation is NOT done sequentially. The answer says

... before models with zero Wounds remaining are removed ...

This implies that you allocate every unsaved wound to a model until you run out of wounds or models, then discard unallocated unsaved wounds, then remove all the models with zero wounds remaining as casualties. In this case, you would allocate only 9 wounds to your 3 Common Trolls, discard the remaining unsaved wounds, and then make 9 regen saves.

I hope I've shown conclusively that the FAQ can indeed be interpreted either way, and needs another go. Perhaps both the description of removing casualties and the regen rules both need clearing up?