No. The Xbox 360 never had a "Silver" membership tier.
Actual Xbox 360 Tiers
Xbox Live Free (called "Silver" colloquially): Profile, friends, achievements, marketplace, demo downloads. **No online multiplayer.**
Xbox Live Gold (Paid): Online multiplayer, Games with Gold, party chat, early demos, discounts.
Confusion Source
Xbox One used "Xbox Live Gold" + "Xbox Live Free" (later "Xbox network").
Xbox Series X|S: **No Gold required for free-to-play games** (Fortnite, Apex, Warzone). Gold only for paid-game multiplayer.
Xbox Game Pass Core (replaced Gold 2023) = Gold benefits + game catalog.
Today on Xbox 360
Most game servers dead. Gold only needed for few active titles (Minecraft Xbox 360, Dark Souls via BC on newer consoles). Free tier allows demo/theme downloads, profile management.