does impedance limit the current in a transformer?
In a transformer, the inductance of each coil is measured as the inductance with the other coil forming an "open circuit."
When you short the secondary coil in a transformer, the inductance of the primary coil drops dramatically.

If I understand the intent of your question correctly, this is where your intended use of a "high impedance" (although it'd be correctly stated as "high reactance" or "high inductance") primary coil to limit overall transformer current flow will break down.
In order to limit the max. possible output current of your transformer to a certain value, the resistance (not reactance, just resistive losses) in the coils and the magnetic losses in the core+coupling between the two coils would have to be great enough to limit the current to that amount.
This would, unfortunately cause highly inefficient operation, high losses, and likely the overheating that you are wanting to avoid.