Yes you can program the car to charge at these times as well but every time you go charging elsewhere, you have to tell it to start charging every time.
Clarification ... that's not how it works. Despite my charge point having the facility to control charge times I choose to have the times set by the car. This does not mean that "every time you go charging elsewhere, you have to tell it to start charging every time." If I plug into a public charger or a Tesla Supercharger it starts charging immediately.