All of the line output transformers I have ever seen need some kind of load, but its not so much for transient response as for flat frequency response.Proper transient response and flat frequency response of course go hand in hand, especially in the HF/ultrasonic region, where a poor quality transformer tends to resonate.
But for a bit of perspective, I pulled out a John Hardy M-2 mic preamp and ran a couple of sweeps. This uses a Jensen JT-11-BMCF output transformer, and its response deviation between 150, 600, and 100K loads were all within +/- 0.1 dB of each other from 20Hz to 50KHz. Measuring the AP System One itself (Bruce Hofer's patented transformer output circuit) delivers virtually indistinguishable performance into all three loads (less than +/- 0.01 dB of each other) from 20Hz to 200KHz.
Pretty good for a bit of iron, eh?