HT Games
No. The Xbox 360 Pro (20 GB model) box contains only the hardware: the console itself, a power supply, an AV cable (composite/component), and one wireless controller. Xbox Live Gold must be purchased separately to access online multiplayer, Games with Gold free titles, and party chat features.
Gold subscriptions were sold as 1-month, 3-month, or 12-month codes (physical cards or digital codes). Note that Xbox Live Gold has since been succeeded by Xbox Game Pass Core on modern consoles, but for the original Xbox 360, a separate Gold subscription was always required for online play.