"Should" is the word to think about. When there is a should in your question, then you need to really ask yourself "why" should she ... and then make a decision. Yes, I want to limit her and have her do other things, or No, I think I and she can manage without limitations for now.
You say "she's not doing anything productive other than the HW..." - so are you saying you want to make her more productive? If so, productive in what? Be confident and know what you want. If her 4 plus hours of screen time is a concern to you (implied since you asking about it) then, what change or option to you have to offer her?
If and when you choose to limit your child's screen time or anything else, be certain on the why, and be ready to discuss other options.
One thing about summer breaks: As many of us follow the education statistics, summer is a time where a lot of student forget what they learn, and are not stimulated enough, thus needing to catch-up often when they return. If school is around the corner, then this is a good time to start to limit, because she needs to re-learn the habits and actions of "school time"... and that includes sleeping at appropriate times.
Good luck