If you get a Cloud Camera - like Nest, Ring, Arlo - then for full functionality they will need
1) Internet connection to work
2) Cloud service to work
3) and of course your WiFi router to work
This means, YES your internet takes a hit.
If you get a wired IP PoE camera - like what most of us prefer here, then there is no hit on your internet as #1 and #2 do not matter if you are viewing at home via the wifi or wired ( like on a PC )
( #1, and maybe #2 depending on how you use it will matter if you view remotely )