Spiders hatching out while you're away would be terrible. They might jumpstart the car and drive away! :lol:
The spray might still be lingering in the airducts when you drive it and then you'd be inhaling it, so I wouldn't go crazy with the spray. Don't have an alternative plan though as I don't have that problem here.
Also, there may not be spiders in NZ, but I remember that there was a big problems with Kea's in the South Island. They had a taste for rubber and windshield weatherstripping! How do you defend against that?!