Fabio,

>INDEX RAND() TAG T_RAND

rand() is quite different than datetime() because each row will have a distinct value subject to the limits of the pseudorandom number generator.

>With DATE()/DATETIME() is possible do more complex operations.

Like what? You are creating several keys with the same value so the usefulness of your complex operations seems somewhat suspect. Such an index would be no different than the natural order of the table.