From a rules-system point of view there is no real reason why it shouldn't work. The templates are more like examples of possible character types in any case. So you could theoretically create the "Pink Court infected Virgin" :-P A White Court Virgin with a Red Court Infection.
It doesn't fit into my understanding of the Dresdenverse though.
But lets say it could happen, then that's how i'd picture it:
1. A full White vamp would be protected by his own demon against the invading Red-Demon.
2. A White court virgin... i'd say having two demons battling for control in your mind, soul and body... only two outcomes here, either you go hopelessly mad, or one of the demons takes charge and destroys the other completely.
So, technically possible, but imho not fitting for the Dresdenverse.