ok, fine, I looked it up: 1080i was the max it could go but most of the latter Xbox games were designed to run in 720p.
(care of wikipedia) here is the tech specs for the GC:
Graphics processing unit:
162 MHz "Flipper" LSI (co-developed by Nintendo and ArtX, acquired by ATI)
180 nm NEC eDRAM-compatible process
8 GFLOPS
4 pixel pipelines with 1 texture unit each[14]
TEV "Texture EnVironment" engine (similar to Nvidia's GeForce-class "register combiners")
Fixed-function hardware transform and lighting (T&L), 20+ million polygons in-game[16]
648 megapixels/second (162 MHz × 4 pipelines), 648 megatexels/second (648 MP × 1 texture unit) (peak)
Peak triangle performance: 20,250,000 32-pixel triangles/s raw and with 1 texture and lit
337,500 triangles a frame at 60 FPS
675,000 triangles a frame at 30 FPS
8 texture layers per pass, texture compression, full scene anti-aliasing[16]
8 simultaneous hardware light sources
Bilinear, trilinear, and anisotropic texture filtering
Multi-texturing, bump mapping, reflection mapping, 24-bit z-buffer
24-bit RGB/32-bit RGBA color depth
Hardware limitations sometimes require a 6r+6g+6b+6a mode (18-bit color), resulting in color banding.
720 × 480 interlaced (480i) or progressive scan (480p) - 60 Hz, 720 × 576 interlaced (576i) - 50 Hz
and the Xbox:
GPU and system chipset: 233 MHz "NV2A" ASIC. Co-developed by Microsoft and Nvidia.
Geometry engine: 115 million vertices/second, 125 million particles/second (peak)
4 pixel pipelines with 2 texture units each
932 megapixels/second (233 MHz × 4 pipelines), 1,864 megatexels/second (932 MP × 2 texture units) (peak)
Peak triangle performance (32pixel divided from filrate): 29,125,000 32-pixel triangles/s raw or w. 2 textures and lit.
485,416 triangles per frame at 60 frame/s
970,833 triangles per frame at 30 frame/s
8 textures per pass, texture compression, full scene anti-aliasing (NV Quincunx, supersampling, multisampling)
Bilinear, trilinear, and anisotropic texture filtering
Similar to the GeForce4 Ti4200 PC GPU in features and performance
Resolutions: 480i, 480p, 576i, 576p, 720p, 1080i
I bolded the applicable parts, my point is that it it was POSSIBLE even back on the Gamecube.