Making sense of transformer measurements

[Mark Johnson]

I am wondering if I can measure it while the PSU is powered off, and inject signals of various frequencies via a 1k resistor directly onto the secondary winding terminals. I then use a scope to probe on various points on the rails and observe any peakings.

Would it work?

Build it and find out!

Or, explore it in circuit simulation first. If the simulation results look promising, build a prototype and find out.