That must be what is going on because in the vinca ground cover I have found numerous young seedlings where some of the fruit likely dropped. Apparently birds will eat some berries but others make it ...
I would have tall perennials planted and then the ground cover. Most of the time basic spacing ideas were ... Some of the common groundcovers are myrtle/vinca, pachysandra, lilyturf, stonecrop, ...
It is a good bet that the most limiting factor in the course of a lawn’s future is the availability of sun as the shade trees ...