You never know . . . to be honest . . . but in general, if a well established theater company that produces regularly posts looking for SMs for an entire season - that's a red flag that they are fulfilling a requirement. For example, La Jolla Playhouse knows where to find stage managers, often using Broadway Stage Managers for their larger shows, and isn't short knowing where to find stage managers.
Usually, I would say . . . anytime there is a posting that is posting the entire season is farming for resumes, and fulfilling their requirement.
No, having worked for large regional theater and have been on the receiving end of these resumes - it doesn't mean your resume will go unnoticed.