Received harassing hate mail from Xbox User [Mod removed] - messages were not deleted; user...

As long as you reported them, the enforcement team will investigate them and take the appropriate action. They do not use the forums. If you haven't done so already, you'll also want to block communications with them.

If you're being harassed on Xbox, the BEST thing to do is report any messages, block, and move on. Microsoft can't punish these type of people if you're not reporting the user, especially if they're sending messages. If their messages include anything
that can be deemed offensive and/or harassment and they were properly reported, they'll more than likely receive a communication ban at minimum.

Will you Marry me? ^^^^^^^^

could be weeks, months, years, or not at all. They have to sort through millions of "XxWhoeverxX called me a hurtful word! Ban him!!" messages that pour in like a tsunami. Your complaint probably won't even be seen for a month. Just suck it up.

Once again support have provided the wrong information.

The forum has a 'no name and shame' rule. So posting the user's gamertag on here is actually more likely to get you suspended from the forum than it is him from Xbox LIVE.

You've done absolutely the right thing by reporting through your console. It is now just a matter of time until the Enforcement Team investigate and take appropriate action.