The most likely failure mode of a power supply transformer is for it to open, so if there's continuity, I'd feel pretty comfortable powering it up. A technician might use a variac to apply power slowly, measuring the voltage output on the secondaries after verifying that the windings weren't open. A drastically low voltage condition indicates that windings are open. With the input power at say 1/4 line voltage, you'd expect the secondaries to all be at 1/4th their voltage rating and if that weren't the case, the transformer might be shorted. But like I say, the most common failure mode is open windings.