Do large non-pressurized metal planes have a maximum fatigue cycle?
Yes they do, and here is why. 

Airplanes are made mostly of aluminum rather than steel. It is possible to design a steel part in such a way that it will never succumb to fatigue failure (crack propagation at a stress significantly below the yield stress) but this is not true of aluminum and its alloys. For this reason it is necessary to periodically tear down and inspect aircraft for fatigue cracking of their aluminum structure- in essence, safety is inspected into (aluminum) aircraft because from a design standpoint, it is not possible to design fatigue failures out of their structure. 

During that teardown, any part that shows fatigue cracking (or corrosion, or physical damage, etc.) is removed and replaced with a new part that is certifiably fault-free. To some extent this means that a DC-3 with 40,000 hours on it has had so much of its structure replaced over the years that the joke is told that the only part that actually has 40,000 hours on it is the serial number plate. 

Flexure of the structure during turbulence in flight is a more significant source of fatigue cycling than cargo loading &amp; unloading cycles.