The medium is the message. If we detected a modulated signal in gravitational waves, it would be like an Iron Age tribe receiving a 100 foot tall perfectly polished stainless steel statue with ornate inscriptions and pictograms. It would be recognizable and within our conception, but it would also be a demonstration of development and access to resources beyond our imagination. That's the upside. In a galaxy of sparse and sparingly advanced civilizations, the message might be "fear us and stay away" in a way that EM would not convey.