There is the link at the bottom of my United email:
You're enrolled. Earn 1,000 miles with your first meal.
So I clicked on it (being already logged in into MP dining) and it allowed me to register to the bonus: "Earn 1,000 bonus award miles for creating an online profile. Exclusively for MileagePlus Visa CardMembers"
It registered for the MP account with and without Visa.
Of course YMMV