What would happen if the zygote did not implant in the uterus?

Passes out. A non-implanted zygote, like the millions of fertilized eggs in normal physiology that do not implant, will either degenerate or pass out and cease to exist. The uterus will remain normal and ready to accept another fertilized egg when the opportunity presents itself.
Debated. It was not a question about when does pregnancy begin? Lol if she were an ivf patient and implantation did not occur you'd tell her nothing happened? That's helpful especially since you weren't there with your micro eyes to see what exactly happened. I'll stick with early miscarraige thanks for patient understanding.
Nothing. Pregnancy is defined by implantation not fertilization. If implantation does not occur after fertilization, the zygote would pass with the menstrual blood. This would not be considered a miscarriage because implantation never occurred.
Early miscarriage. Period may be a few days late, but nothing exceptional would happen otherwise and no way of ever knowing as period can be late due to many factors.