You can install the Android Market on a MID that doesn't have the Market installed on it. It's not, however, as easy as installing the proper App. In most cases the process includes Root access and then installing the Google Framework APK and then the Market APK. You then need to configure the market to work by fooling it into thinking that it's actually installed on a supported device.
Your best bet would be to do a search based on your particular MID to find examples where others have already done this... and then just follow the steps that they followed.