Unless the action starts to yield.
The 6mmBR case head is much stronger than the OP 308 case.
The 308 primer pocket will become loose somewhere between 72kpsi and 78 kpsi [unless it is Lapua Palma small primer pocket brass]
The 6mmBR brass will not give up the primer pocket before the thickest small rifle magnum primer [CCI450] will pierce. That happens somewhere between 80 kpsi and 90k psi.
I have reached that with the 1917 Sav99
That threshold of primer piercing is dependent on the firing pin to firing pin hole fit. GreTan offers a service of bushing the firing pin hole to get that threshold higher.
But I would bet money no one has sent GreTan and old Sav99 bolt to bush