With Earth's day length becoming irrelevant, the 24 hour clock becomes irrelevant too, and the length of the sleep cycle may shift.
We could eventually arrive at stardates with one starday being 100000 seconds. Of course, that would be just as arbitrary as simply keeping the 24 hours of 60 minutes each.
They were very limited, though. We do not really know what would happen on a spaceship that changed its day to 100 000 seconds and subjected the crew to this cycle for months or years.
Given how adaptable people usually are to external influences, I would guess that some adaptation would take place.
To my knowledge, once you take the sun away, it tends to drift more towards 25 or 26 hours. And that's in humans who experienced the externally imposed 24 hour cycle for decades before participating in a short experiment, not potential spacefarers born onboard of stations or ships.
We could eventually arrive at stardates with one starday being 100000 seconds. Of course, that would be just as arbitrary as simply keeping the 24 hours of 60 minutes each.