I'm sure others will have some more specific info for you, but it's a matter of trust and insurance to my way of thinking. Are you comfortable with them driving it? Probably, since they built it and have had it in the past.
I would imagine that if anything happens to it while in their care, they would cover the repair replacement costs. Even though YOUR insurance will cover some things, that's your money and your record. I'd expect them to cover 100% of anything that goes wrong. From a chip in the paint, to a dented fender, even down to cleaning it up if they let kids with dirty fingers crawl all over it!
I bet a lot of shops do just this with customer's rides, so it's likely a regular thing. Maybe they've even done it. But don't just let them run it around without some assurances (preferably in writing) that they will take good care of your baby. AND you!
Paul