Sure, except all the assumptions before drawing the conclusion that "the diode can't be damaged if tested like this" might have not been true. For example, can you bet your head on that resistor being indeed 1k, as it was drawn, and able to dissipate 1.5W? I wouldn't, but we are nitpicking already.
Also, there is no auto mode in a DMM diode testing mode. No diode "range" is switched automatically depending on a measured diode, like the voltage range is switched automatically depending on the measured voltage, or like the resistance range is switched automatically according to the measured resistor.
Since the diodes probing was sorted out, any further details will just add confusion.
Have a nice ride with that bike!