Before regaining Savoy, Emmanuel-Philibert was governor of Netherlands. So, I guess he and Elizabeth would live there, not in England, during the end of Mary's reign.
Of course, with Mary's death, Elizabeth would come back to England to take the crown.
Then, I am pretty sure she would do the same thing as in OTL: make England Anglican again.
What would Emmanuel-Philibert do? Would he convert to Anglicanism and join Elizabeth in England?
If so, they may have some Anglican children to inherit England, which means no union between Scotland and England. But Emmanuel-Philibert would likely lose any chance to regain Savoy if he converts to Anglicanism.
If he refuses to convert, he would probably stay in Netherlands and Elizabeth is likely to do the same thing as her father: an Anglican annulment of their mariage.
An open question, if Emmanuel-Philibert does not convert, is about the potential children. They may have one or two children before Mary's death. Would Emmanuel-Philibert accept to send them to Elizabeth in England? Or would he keep them in Netherlands and raise them as Catholics?
The last option might lead to a quite interesting situation. Even if Elizabeth excludes her Catholic children from the succession, most people in England would probably see them as her legitimate heirs. Also, the Spanish would support them.
Of course, the logical Catholic claimer would still be Mary Queen of Scots as Elizabeth would still be a bastard in the eyes of Catholic canon law.