I just started shooting some carbon arrows yesterday and they are faster but they group the same as my allum without ajusting my sites.
In some cases, yes. It depends on the diameter and spine of the two shafts being compared. If they are both similar then I see no reason why they should not group relatively close together.
I had two carbons of different spines with different points and different overall weights group at the exact same spot so I see no reason why a similar situation could not occur between a carbon and an aluminum arrow.