I'm certainly no expert, but I do have similar siding on my house.
I think the thing I would worry about with your plan of nailing through the piece of siding above is weather intrusion. In theory (I'm guessing here), rain could fall on the piece of siding above, trickle down to the nail, follow the nail through the upper piece of siding, the broken piece of siding, and into the sheetrock underneath.
The other thing to think about is that it just sort of looks ugly to do it that way. If you later go to sell the house and someone notices your repair, the repair itself might not be a big deal but buyers often wonder, "If they did this one weird thing, what other weird things did they do to this house and what might be the feared consequences of those multiple weird things." So it could damage your resale value.
I'm sure this has happened before. I'd call a siding contractor and ask them how they normally fix it. They might be willing to tell you over the phone. Or you can also ask at Home Depot or Lowe's.
Good luck!