Yes and no. You can control whether you have a badge count or just a visual indication or nothing at all, but it is done on a per-class basis. For example, you could set it to just put a dot next to project or context names where you have actions that are available but not yet due soon or overdue, and have the counts for those which are. You can read about how to do this
here.
As far as I know, there is no way to prevent actions in one class of projects from showing up in badge counts, which seems to be what you are requesting.