As someone who's run a chemistry lab for almost a decade, I've dealt with my fair share of compressed gas leaks. You are correct that if you pressurize a closed system, it should hold pressure even if the supply is turned off. So yes, if you connected an empty keg, took it to 14 psi, then closed the valve on the tank, then it the line should hold that. Now if the keg is full of beer or water, thats another matter (it might absorb the CO2).
Leak detecting is a slow and painful process. If your line doesn't hold pressure, this time re-pressurize the keg, and close the valve on the regulator instead. Continue to work your way down the line in a methodical process. You're also correct that at fridge temps the high pressure dial is useless. Note the tare weight on the tank, then go weigh it on a set of bathroom scales and note the difference - I use that process to gauge how much gas I have left.