Yes it is a thing.
Two years ago I had trouble with another car - Ford Falcon - 6-cyl car. If not used for a week, the battery would die off to the point where starting was nearly impossible. Of course, I blamed the battery, and after spending another $200 local money....I was proven wrong.
Without testing, I decided that the starter must be the cause of the parasitic draw. So I arranged to have it replaced. Upon removal and subsequent opening up of the original starter motor, a large amount of carbon dust was found inside. This explains the draw....the carbon was sufficient in quantity and coverage to actually provide a path for the voltage to track from the solenoid through to ground - causing a reasonable draw of current.
New starter motor was fitted, car leapt into life, and now the car can be left for a month, and it sounds like it was last used the day before.
So, yes, a starter motor can be the parasitic draw, and a substantial one at that.
Here's a picture of the car taken by a local enthusiast......
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