If people get annoyed because you are keeping them in the loop, you have a different kind of problem...I hope that doesn't happen.
I think it is a fantastic idea!
I would go a step further and recognize any alum who show up during the month in the following news letter. It may help increase alum involvement.
My husband's fraternity sends him a quarterly newsletter. It is now around 8 pages long. I can tell you that it is both welcome and read. They talk about new members, chapter successes and challenges. They also have alum write about their memories.