No. The PlayStation 3 and Xbox 360 operate on completely separate online ecosystems. They cannot connect to each other for cross-platform multiplayer.
Each service manages its own friends lists, matchmaking servers, digital storefronts, and security infrastructure. There is no technical bridge between them on these legacy consoles.
Note: Cross-play became feasible in later generations (PS4/PS5, Xbox One/Series X, PC), but it is not supported on PS3 or Xbox 360.