That would not bring as fast and as effective results as a large sign in the garage saying, "Jesus Christ came into the word to save sinners (including HOA members)."
The HOA could also be charged with being sexist and insensitive, since men are responsible for the majority of garages, and would be most offended by leaving them open.
There are quite a few possibilities to teach the HOA a lesson. Perhaps knowing something about the HOA busy bodies would help determine which possibility is best.