I myself have had mixed results. Sometimes editing the caption penalized me. Some other times gave a boost in terms of people reached by adding a few hashtags.
I don’t think that this will affect your posts unless you change the caption in a drastically worse or better way. For example if you have a completely unrelated caption to your post, changing it to something that fits might increase engagement.
However, from a purely technical IG perspective, I wouldn’t see why it would have less or more engagement just because you changed it.