They do but it gets complicated with how they calculate your premiums.
Even with the car suspended it costs around $20 per month. Not much but it adds up over years. They also don't like you to suspend coverage for the whole year. Honestly, if I didn't have to get an appraisal done to put insurance on it, I'djust leave it uninsured while stored. No one's going to steal it and it's not worth much anyway.
I asked my agant before i left for my trip and thats what i was told. I'll try asking another statefarm agent.