This is just an anecdotal data point but my mother was bilingual and near the end of her life had a stroke. It impacted her language-- but mostly for English, not nearly as much her native language. She could understand both English and Italian, but would almost entirely speak Italian, not even realizing which language she was speaking. Is that a "cognitive advantage"? Maybe? I am not qualified to answer that. But to…
*For completeness, according to current neurolinguistic models it's more complex than that, more brain regions are actually responsible for speech/understanding.