As long as the moisture content is reasonably low, they will burn. The problem you may face is
feed rate and airflow through the fuel, since the J-tube is designed for sticks or
kindling with gaps around and between the pieces. Corn, like pellets, small
wood chips, or sawdust, will pile up on the bottom of the feed tube and create a non-burning zone where the air fails to penetrate. The next thing that happens is you lose combustion heat and could run into smokeback and draft issues.
Ask me how I know this....
There are designs that do incremental feeding of particle fuels, so it's definitely possible. You just don't want to dump a bunch in at once. Check the recently active
thread on the Liberator heater and their pellet feeder for ideas.