No. The Xbox 360 cannot play HD DVD discs with its internal drive.
Drive Capabilities
Internal Drive (All Models):DVD-ROM only (DVD±R/RW, CD-R/RW). Reads dual-layer DVD (DVD-9) for games/movies.
External HD DVD Drive (Xbox 360 HD DVD Player): Released Nov 2006 ($199). USB 2.0 external drive. Plays HD DVD movies only (not games). Discontinued 2008 after Blu-ray won format war. Rare/expensive used.
Blu-ray:Never supported. Xbox 360 lacks blue laser diode and AACS/BD+ decryption hardware. Xbox One / Series X|S play Blu-ray.
Video Playback on 360 (Native)
DVD-Video (MPEG-2)
DivX / XviD / H.264 / WMV (via USB / Network / Disc — Fall 2007 Update)
No HD DVD, No Blu-ray.
If you have HD DVD movies, you need a dedicated HD DVD player (Toshiba, Xbox 360 External) or a PC with HD DVD drive + AnyDVD HD (decryption) to rip/convert.