It is possible, if you saturate your upstream connection to more than 80%, you will start to see downstream speeds suffer. The downstream needs to send a certain number of upstream packets as part of how TCP/IP works. If it isn't able to send these upstream packets because the upstream is saturated, your downstream speed will be choked.
The only way to stop the camera from talking on the upstream side of your connection is to block them from having internet access. However, this isn't reasonable if you like to view the cameras remotely when you are not on your home network.
You may also want to look into something on your router called QoS or Quality of Service management. You can set the cameras to a lower priority than your computer system, so if your upstream becomes saturated, it will prioritize your computers upstream and downstream data over the cameras, so you connection with your computer won't be compromised.