Will zero pressure in a propane line cause a leak when the pressure returns
I've been a gas fitter for over 20 years and worked with it much of my childhood before that. That is a completely false statement. I think it's just an excuse to get a tech in your house to see if they can generate a sale. You can almost blow with your mouth the amount of pressure that a propane system will see. After the second stage regulator the pressure is commonly 11" water column. Can you blow water up a 12" straw? Probably. Then you can blow more pressure then what's in your piping system. If a leak were to develop after "losing pressure" then it was extremely loose to begin with and wouldn't have passed the original 15 psi pressue test. 15 psi is 420" water column.

What about when the temperature changes in the house? The expansion and contraction of the fittings would be greatly more significant than a 11" pressure drop. What if you bump into the pipe? Also pipe dope is primarily a anti-seize agent not a leak sealant. It does effectively help seal poorly made threaded connections but that's not its job.