Hi Bill,
What you suggest does sound feasible, the garlic pulling wont disturb corn roots enough to cause a problem.
However i've really got to ask, if you've only got 5'x12' to work with, why would you plant corn? If it does really well you might harvest 30-50 ears from that space. That would cost you $20 to buy from an organic farmer that has acres to spare.
Instead you could grow salad, tomatoes, etc to eat all summer with tomato sauce to can for the winter.
Anyway, just my 2 cents. I grow veggies on a half acre and barely allow myself space for a little corn, other plants are just more space/fertility efficient.

I can see two problems with that plan right off: first, corn is a very heavy feeder, it could starve out the garlic or on the other hand, garlic is a pretty heavy feeder when it comes to nitrogen and it could starve out the corn. Second, the garlic needs to be allowed to dry out completely before harvesting. If kept wet it will continue to grow and will not store well for you.

And, yes, I believe it will be a huge mess, corn roots would be disturbed if not already strangled by the huge, thick mass of roots the garlic will put out. Plus, it would be a huge mess planting the corn, I'd think, when the garlic is already up and growing and you risk harming the garlic roots not to mention the precious bulb by digging around to plant the corn.

Any reason you don't grow in containers? You could put garlic in large containers and have your frivolous fun with the corn in your one bed.