Doubtful.

I think the other way around as the viburnham is much stronger growing and will eventually shade them out

Agree the viburnum is rather more likely to kill off the periwinkle

I would say that if your periwinkle is vinca minor, then they will do well together as the vinca will cover the ground beneath the viburnum. If it is vinca major, then it will become very invasive and end up all over the garden.