multisite stability with plugin conflicts


just a very general question here.

if there is a conflict/issue with a plugin/theme on the main site and that main site basically shows a white screen with php error messages etc, will that cause all sites on the network to go down ?

will it make a difference if the plugin in question is not network activated or used on the other sites ?

what about conflicts/issues on sub sites ?

basically i am trying to get a better appreciation/understanding on how and when conflicts/issues can affect an entire multisite.

when reading reviews on blogs about pros and cons of WP multisite they would usually say something like "issues on the main site can affect the entire network" but this is pretty general and i would like to get a bit more specific feedback.

any experience in this shared would be greatly appreciated.
kind regards.