Will an aftermarket backup camera work with my factory infotainment screen?

Sometimes, but not plug-and-play in most cases. Many kits in this category ship with their own dedicated monitor for that reason. Integrating into a factory head unit usually requires a vehicle-specific interface module or an aftermarket stereo that accepts a composite/AHD camera input. The cleanest path for most buyers is to use the included monitor or a mirror-mount display.