No my tank will get cold and a little icing at the end of a long boil but not to the point where it ceases to flow. You can always put a fermwrap on the propane tank to combat this problem.
On my old aluminum rig (which had a 1/2 NPT pipe gas manifold), I used a 1/2 FNPT to 1/4 swage tube so what you are proposing is perfect. Find a 1/2 to 1/4 whatever fitting you can and make sure the hose is the same fitting. No need to buy a braided line just for test, a rubber hose will suffice and will save you cash.
On my old aluminum rig (which had a 1/2 NPT pipe gas manifold), I used a 1/2 FNPT to 1/4 swage tube so what you are proposing is perfect. Find a 1/2 to 1/4 whatever fitting you can and make sure the hose is the same fitting. No need to buy a braided line just for test, a rubber hose will suffice and will save you cash.