MC is not going to continously monitor your files, it would only compute this during audio analysis - at which point it could notify you that something changed. Not sure a date field helps (or even the "CRC changed" field), since its not doing checks unless you ask it to check, and can immediately let you know then and there.
All that said, I view the CRC more generally useful to check rips or conversions, if you are worried about file corruption, the file system or the OS would probably be better equipped to monitor that on a regular basis, since verifying a file changed is faster if you don't also parse and decode the audio. My file server checks a portion of my files every night for integrity, and it gets through all files every few weeks that way.