If I check for resistance on the output end of a unpowered transformer, am I correct in assuming I should NOT get a reading. That if I do get a reading there is a short in the transformer somewhere?

A transformer is basically two coils of wire. One coil is the primary (input) side. The other is the secondary (output) side. You should have a resistance in the wires of the coils. So, you should read some resistance on the output ends of an unpowered transformer. If there is a short, the resistance will be less than it is supposed to be.