Here's the answer I got today...I'm not sure if not getting answers is better than this. I gave a clear example of what's happening. So, has anyone who has done this had a player taken off their team and waived after 7 days? :)
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Designating a player removes them from the 40 man roster. Also, a designated player cannot be assigned back to the ML roster, only a minor league roster if they have cleared waivers.
If you designate a player without waivers, then if the player has not been traded/waived after 7 days, he will be automatically waived. If he has not been moved after 10 days, he will be automatically released.