Unfortunately, the voicemail I was transferred to, was not the shop, which doesn't even have a land line.
Bottom line, when I got to the shop they hadn't received my message, and things were a bit of a mess (they needed 2 hours longer than I could leave the vehicle). So, I had to scramble to rearrange my schedule, etc. to make it work.
This is exactly the kind of hassle safelite is supossed to prevent.
All my comments below are about the in-shop experience. The 1-800 part of the service gets 1 star for being polite, otherwise a complete fail.