Does posting with a scheduler hurt engagments rates on Instagram

Summary: it does not

Storrito automates the Instagram Android app to post a story. It is
the same as you would do it manually from an Android smartphone. Therefore Instagram does not note a difference and your engagement rate will not suffer.

However Instagram Stories have some unique features like hashtags, location tags, question stickers and so on. These things leads to more engagement with your story content. Users interact with those elements and even contribute via polls or questions. Especially hashtags and location tags are a must-have, since your story post might get featured in the corresponding hashtag (example) or location feed (example). Via these feeds thousands of other user might see your story content, even when they do not follow your Instagram account yet. 

For that reason you should use a scheduler like that
supports these unique Instagram Stories features to drive up your engangement rate. As far as we know is the only service that offers these features at the moment.