Yes, I've done that, and that works just fine.
Also, I should update my previous post and say that since that day I have not had a single issue with exceeding daily message limits.
Oddly, I had already verified and done all the other multiple-layer security theater steps the day before I had the message limit problem. However, it appears that it required longer than I expected for the limit to be lifted.
I advise patience to new account holders. Definitely verify your account and all that, then be patient for a couple of days until the limit is lifted.
At least that was my experience. I wouldn't dream of speaking for Microsoft, and can't guarantee those results for others.