only abs codes are stored in a history, i know some of your normal scanners on some cars will read abs codes, but they cant clear or see the history of every code thats been set over time.
if a abs code comes back after clearing, its a actual fault. even if its not setting the abs or brake light on.
if the module is shorting it's not going to save anything, that's why I said "maybe" really depends. A lazy or funky sensor could also cause a problem and not set a code. you might commonly see that happen when coming to a stop and just before a full stop the abs activates and pulses the brake pedal, it's doing that because a sensor is not giving correct data but yet is not off enough to trigger a light or throw a code it just thinks a wheel is slipping.
I have seen both of these instances happen more than once.
other people have reported the same, abs light comes on and goes off, maybe random on/off, yet no code stored.
which is why I always tell people to scan while the light is on or before shutting it off after the light has come on
same with the traction control that is another self-checking system in general it only activates with wheel slip (other problems CAN make it error) but, once it see's all is well it's off