Should non Instructional Designers edit Storyline courses?

For decades, centuries, even, colleges and universities have subscribed to the idea that the main determiner of academic success is the subject expertise of the teacher. In very recent times, most of them have come to the realization that teaching ability has as much, or more effect on how learners learn. Rather than taking on the very daunting task of training their professors (some of whom already are very skilled teachers) to teach, they have brought a new class of helper alongside them. That's where the concept of ID's came from. They are the teaching and curriculum experts. (Coincidently, that's why landscape, graphic, bridge, and other designers are not good choices for designing instruction.)  Business is way ahead of academia in discovering and implementing this.

With that as background, I'm going to make a bunch of assumptions about your questions, and try to answer them.  It sounds to me like you have courses that have been through the design stage, and are aligned with the curriculum, storyboarded,  through the initial stage of development, and in the hands of the e-authoring or development crew. Also assuming you have considered and solved Judy's concerns about licensing and SL ability.Those people typically have a backlog of several months or more, and you are looking to ease their load, specifically with spelling, grammar, phrasing, quality assurance, and other post-design tasks - tasks that almost anybody in your organization can do, especially if the edits are laid out for them. It is a given that no matter what their title, all of your people will differ in their level of design, authoring, teaching, communication, grammar, and spelling skills. Some will be better than others. That may be the starting point for your decision.

Know first, that if these are either in-person or hybrid classes, the trainers will modify them on the fly to fit the audience, the way the class is flowing today, and their own personality. Keeping them from making edits likely won't gain anything.

Admittedly, I come from an academic background, but in general, SMEs probably have more important things to do. By important, I mean tasks that only they can perform. It makes sense to prioritize tasks on the basis of the expertise need to perform them. Then assign the available personnel to the highest level task they are qualified for. For example, anyone can change a "." to a "?" at the end of a quiz question, but not everyone can create valid quiz questions. 

To me, the important considerations are: Is this person capable of this, and is it the best use of our resources.