This would depend entirely on what was pulled out. The boxwood should present no problems, but other shrubs are capable of resprouting from their roots.

Yes, may as well just go ahead with the new planting. I can't say for absolute certain, but I suspect you will not have much of any issue with whatever's been left behind.

+oM

Crape myrtles, some yuccas, and Myrica cerifera are several plants that can grow back from root segments. So as they say, it depends on the plant.