plated via on roger pcb 5880
Your questions can be answered in general from the respective Rogers fabrication guidelines. I understand from a short review, that your design should be feasible.
But, apart from the general technological option, it has to be managed by your PCB manufacturer. I know of cases, where even leading international manufacturers simply ignored the Rogers guidelines, resulting in catastrohic failure.
0.062" is the nominal 5880 dielectric thickness, whatever one may suppose to be usual.