The only advantage to using corn that I can think of is that you get corn to eat, which is a good plus.
Other that that, the beans will likely outgrown the corn, or you'd miss a good part of the growing season waiting for the corn to get tall enough. The corn would tend to shade out the beans' leaves. The corn isn't very tall and can't be moved around or modified like a teepee. If you want the best beans, give them as tall of a support, within budget and reason, as you can.

Several potential problems - common to all variations of a 3 sisters planting. In addition to all the problems listed by tcstoehr -

1) corn requires much more nitrogen than beans do. Too much nitrogen gives you lovely bean plants with no beans on them.

2) pole bean vines are quite tenacious. They can easily choke corn and pull stalks over, even out of the ground.

3) because of the high N needed, corn is an attractive crop for aphids - your beans would prefer to do without them. ;)

You'll be much happier (and so will your corn and beans) if you will use separate, inorganic, supports for your beans.

Dave

Hmmm... I hadn't thought about those things. On the other hand I have very little space and the idea getting corn in addition is really appealing.
If I was going to try corn and beans how much of a reduction in yield could I expect from the beans?
How many vines per stalk? Would it be best to just plant one bean seed every other stalk to spread them out?

You learn by experimenting so if you want to try it go for it. A major problem is few cultivars of sweet corn have stalks strong enough to hold up a bean vine. Corn takes a lot of nitrogen which beans don't like. All vine and no beans. Sweet corn also has a maturity date similar to pole beans. In the olden days of cornfield beans, Field corn (120 day maturity) was used, planted at 42 inch spacing. Big heavy tall stalks that hung around long enough for beans to grow. Even the corn was grown, pretty much in natural soil, with a little manure worked in for nutrients.

I tried planting pole beans with my corn last year and it did not turn out well at all. The beans broke off a lot of the corn leaves as it grew up the corn. The beans grew a lot faster than the corn...and my corn height was significantly stunted.

I am going to try bush beans around the corn this year and see what happens...I started my corn 2 weeks ago and they are about 6 inches tall. I am going to plant bush beans tomorrow...Note...i am planting beans that I will use for dry beans...kidney beans and great northern. THis way i don't have to mess around inside the corn bed....the corn should be done before the dry pods need to be taken off the plant.

Here is a link that might be useful: How my garden grows!

Do all sh2 corn varieties have thin stalks? How long will the stalks stay up after the corn is harvested?