Can Global display be set differently for ByLevel and Overrides? For example, if there are two different teams who only want to see certain levels when working with the file, could Overrides present one team with certain levels on/off and ByLevel give the other team a different combination of Level on/off display?
No, Global Display turns on or off level display in all views regardless of whether overrides are turned on or not. Overrides provide elements an alternate set of element symbology (such as color, Line Weight etc. etc.).
One option to try and achieve this workflow would be to use Saved Views. Different Saved Views can be created to capture the different level states and then applied/recalled at a later stage for use by respective team. To do this, see the Saving Level States article.