Can You Connect an Xbox 360 to a Computer via Dial-Up Internet?
No. You cannot use a dial-up connection (via a computer or otherwise) for Xbox 360 online functionality.
Technical Barriers
Bandwidth: Dial-up (~56 kbps) is far below the minimum required for Xbox Live (256 kbps down / 128 kbps up).
Connection Type: Dial-up is a point-to-point PPP link to an ISP, not a local network (LAN). The Xbox 360 requires a router/switch to communicate with other devices and the internet.
Latency: High ping makes real-time gaming unplayable.
Viable Alternatives
Broadband (DSL/Cable/Fiber): The standard solution.
Mobile Hotspot: Phone tethering or dedicated MiFi device (watch data caps).
Wired Ethernet: Connect Xbox 360 directly to your router for best stability.
Powerline Adapters: Use household electrical wiring for a wired-like connection if Wi-Fi is weak.
Even with a computer acting as a bridge (ICS), dial-up lacks the throughput and NAT traversal for Xbox Live.