My initial feeling is...no. But there are a lot of enrollment/tracking options so you might be able to work around this.
First, a small word on groups and groupings--they are two different things. Groups and groupings are both created at course levels and cannot share between courses. When I want the same group in many courses, I create a csv template for my groups and import them to each course rather than building them over and over again in each course. Then it is one step per course--import group, which saves time if you have a lot of groups (I used to run about 14 groups per course, which isn't a lot until you have 150 courses). The other thing I'd do is if you don't have all your courses set up yet, set up the first course the way you want it, run a back up and then restore it (there is a template to copy courses a bunch if you have a lot to do). You might be able to import groups from one course to another, but that is also a manual process for each course.
Groups allow you to break down results by...well, group. They can be visible or separate. Separate separates visibility for activities if you choose, visible does not. You can set separate at course level, which could prevent non-editing teachers from seeing results of people not in their group, but set visible in activities, letting students see other students work as is possible (like glossary entries or forum posts)--you just make sure course settings are not forced. You can look at course completion by group, activity completion by group, quiz grades by group--very useful.
Groupings are collections of groups (you have 10 groups, you want two of the groups to do something together, you create a grouping and add both groups to it and create activity restrictions based on grouping). In very old moodle (1.9), this was really helpful because you could create activities that were only visible for a particular grouping. But you can do this other ways now (activity restriction for specific group (this or that). It seems like more work to me...but some people like it. I don't believe you can separate participation by grouping, but I could be wrong, as I don't use groupings...ever.
So, on to a work around...I've got a couple ways that might work for you.
Groups + Self Enrolment with Group Enrollment keys. You could set up groups with an enrollment key in every course based on the relevant instructor. You could give each user the key for their group, making sure self-enrollment was specific to groups. Then the non-editing teacher could look specifically at their group. You could probably fiddle it to prevent the non-editing teacher to only see their group (permissions, make sure to assign them explicitly to that group). This would require the non-editing teacher be enrolled with that role in every course. This allows flexibility for students (they don't necessarily all do the same course but they all end up in the same groups for tracking when they are in the same courses).
Cohort enrolments + Groups. If you want to batch enroll rather than self, you could create the groups as above and then create cohorts (site or category levels, your choice--I used to have each fiscal year be a category and would create cohorts in the fiscal year category rather than site level because things would change year to year) based on the instructor (usually I do it by job/program requirements), assign all the students to the cohort and then assign the cohort to the required course, specifying addition into the group. This also would require the non-editing teacher be enrolled with that role in every course. This method would require all students in the group be assigned to the same courses (less student flexibility).
There is such a thing as category roles but these get really tricky and can cause problems. If you decide to go that direction, be cautious and think long and hard about it. I think, by default, only Manager and course creator have category roles but you can, at the site admin level, add other roles to be assigned at the category. I would strongly recommend you NEVER add student to category roles. Students could be added to a category in 1.9 and it caused no end to anguish and aggravation. I am so glad that changed.
There might be other options...but my brain is now tired. My advice--if you have time, play with it. Create a bunch of fake student/teacher accounts and a couple fake courses. Try different stuff. Poke it. I really hope you have both a test/development site and a production site. Try stuff on development so it doesn't mess up production. When you're happy with something, implement it in production. Probably 75% of what I know about Moodle after 13 years of using it was learned by pushing buttons and seeing what would happen. But I'm a button pusher...I know many people have trouble poking things without knowing what will happen.