I think at one time the downgraded jump would appear (and count) as if the higher rotations were never attempted. But they changed that and introduced the << notation.
Yes. There were a few more steps to the changes though.
The very first year of IJS, they were just calling downgraded quads as triples, and downgraded triples as doubles.
Remember also that the cutoff for downgrading at that time was "more than 90 degrees" short of rotation. So it may have looked like a successful quad in real time but showed up on the protocol as a triple.
That did lead to a Zayak problem when a clear 4T attempt was downgraded to 3T and the skater also included two intentional 3T.
So by 2005, the ISU introduced the < symbol to indicate downgrades. There were then two options, fully rotated (within 90 degrees) or downgrade to the base value of a full revolution less, with mandatory minus GOE.
A few years later, they recognized that this was an overly harsh penalty for jumps that might look clean in real time/from different angles, as opposed to being not even close to rotated. So that's when they introduced the distinction between << (downgrade, base value of one revolution less, for jumps more than 180 degrees short of rotation) vs. < (underrotated, 70% of the base value of the intended jump, for 91 to 180 degrees short).
And then several years after that they also introduced the q notation for jumps exactly 90 degrees short, with full base value but a reduction in GOE by the judges.
So now there are 4 different levels of recognition of how close to correct rotation a given jump has achieved, with increasing penalties for more severe lack of rotation.
However, to answer CrazyKittenLady's question, the change from calling the attempted quad a triple (which caused Zayak problems) to calling it a quad with a mark indicating lack of rotation was the first step in refining the notation and penalties for this range of errors.