Security cam wouldn't hook to my slow WiFi, so should I expect the same with a video doorbell ?

@indalay1746 I would say yes but maybe you were told that due to the number of cameras. If that is the case, one doorbell may be fine.
BTW, what is your speed up, down and ping?

You will need approx 2 mbps upload per camera.  
The cameras load up to the Cloud.  The more stuff you have uploading the more upload bandwidth you will need.

Not like a NVR system that operates on the LAN side of your router.