Corn can be broadcast seeded. Your RESULTS won't be too spectacular though. Reason being? Corn needs to be planted at a consistant depth. That depth is determined by a number of factors, including soil type, soil TEMPERATURE (being probably the single most important factor) seed variety, and time relative to the season.
Most corn is planted from 1-1/2" to 2-1/2" deep around my neck of the woods. You could broadcast, then lightly disc it in, but there would be very little consistancy with that.
Another down-side to broadcasting would be weed control. No way to cultivate your crop. You could go with a round-up ready variety, then spray for weeds. Either way, you'll not get much of a crop without some control over weeds.
The thing with a food plot is, you aren't after the maximum yields that a production farmer would be after. Still, you're after some decent "corn" with your crop, and not just stalks. Weeds choke out corn if left un-checked. And in a dry year, weeds can virtually eliminate any chance of decent ears forming.