Do I need to replace attic insulation directly against new framing for a bath fan?
Leaving voids under insulation but outside the air barrier (the drywall, for example) usually results in loss of efficiency. This is because if there's even a small escape path for the air to the unconditioned space the air in the void will cycle via convention, making the area effectively uninsulated. This allows faster heat transmission.

This is why batt insulation is fitted between ceiling joists rather than simply being laid across them. It's usually best to fit insulation directly against the air barrier.