Yes you can. Even if you will only speak, but not share video, you can say "see you....". It sounds better to say, "see you tomorrow" or "see you online tomorrow". If you include "... on the internet...", it sounds strange. You both know that you will use the internet to communicate, so it's not necessary to include this phrase. It is a bit like meeting a friend everyday at a McDonald's restaurant for breakfast - you meet every day of the week. When breakfast is over, you DON'T say "see you at McDonald's tomorrow - you both know where you will meet! This is the place where you always meet!

I'm not sure if you had a question about the preposition "on" for "on the internet". If so, you said it correctly. "on" is the proper preposition to use in this case.