Hydrated lime is used to offset or buffer the pH shift caused by aluminum sulfate. Agricultural lime's slow action is much less capable, if not completely incapable of balancing aluminum sulfate pH swings. So, don't use it in place of hydrated lime.
The primary reason for avoiding a pH shift is fish-safety. Aluminum sulfate is notorious for prompting rapid and, often times, severe pH shifts. I've been told that a pH shift of 2+ points is lethal to fish. I'm not sure what the exact tolerance threshold for fish might be (more or less) or if it varies by specie. But, I know of several instances where fish were floated by non-buffered aluminum sulfate treatments.
