Xbox could encode DTS for games, but it would be pointless since the NVIDIA MCPX (APU) chip handles real-time Dolby Digital 5.1 encoding. For DTS encoding, the Intel CPU would have to “waste” processing power on something that should be handled by the APU. The whole purpose in having dedicated processors for graphics and sound is to offload processing from the CPU.
For interactive real-time sound in games, the audio stream is encoded in real-time. It’s not stored encoded on the DVD. Only sound samples must be stored on the game DVD, but pre-encoded Dolby Digital 5.1 sound streams are not required.
Xbox can pass through DTS sound from DVD movies using appropriate software. That means already encoded sound streams stored on the DVD can pass through to a DVD decoder. For real-time sound in Xbox games, it's very unlikely for any game developer to choose DTS over Dolby Digital.
Afterall the Xbox is really a PC if you didnt know already.