The simple answer to this question is: No. MVP '06 College Baseball for Xbox cannot be played on an Xbox 360.
While the backwards compatibility - referring to a game which can be played on a newer version of a console; like PS2 to PSone, or Xbox 360 to Xbox - list for the Xbox 360 is extensive, MVP '06 College Baseball is not covered.
How Does Backwards Compatibilty Work?
To achieve backwards compatibility, each old Xbox game needs an 'emulation' program to run. For the 400+ titles that ARE backwards compatible with the Xbox 360, these have been written. But for MVP '06 College Baseball, they unfortunately have not. Microsoft usually decides on which games to make backwards compatible based on previous sales. For example, a game such as Halo 2, which sold millions of units upon release, will definitely get the backwards compatible treatment (and definitely has). MVP '06 College Baseball probably didn't get the sales required to deem it worthy of Microsoft's second attention.
How Can I Get Hold Of These 'Emulation Programs'?
The emulation programs can be downloaded through the Xbox Live service or from Xbox.com and burned on CD or DVD recordable media. They are also routinely distributed as part of the content on the Official Xbox Magazine monthly discs. The profiles are downloaded as a single bundle, and hence only need to be applied once per update (if doing so offline), or are automatically downloaded the first time a compatible game is inserted.
And Do I Need Anything Else To Do This?
The Xbox 360 hard disk is required to play the games on this list. The hard disk is used not only to store the emulation software, but also to store saved games, store downloaded content, and to serve as a data cache for titles which utilize disk caching. Since games for the original Xbox were designed with the expectation that a hard drive would always be available, most titles rely heavily on the presence of one.
So, No Hope For Virtual Baseball Fans Then?
All is not lost for MVP College Baseball fans though, as... GOOD NEWS! The '03 and '04 editions of the game are available for backwards compatibility emulation in the US! So you can enjoy knocking em' for six or whatever it is you do in baseball these days.
FOR A FULL LIST OF BACKWARDS COMPATIBLE GAMES HEAD TO: www.xboxbc.com