I've never played with tubeless bike tires, but I assume there are conceptual similarities to tubeless auto tires. First off, a tubeless tire isn't really tubeless -- there is a "tube" (thin layer of solid rubber) laminated to the inside of the tire to contain the air. Presumably the sealant you have would serve the same purpose, but it's not clear how well.
Second, the tubeless tire has a specially-designed bead area, smoother than a tube-type tire and designed to seal tightly to the rim. Your typical bike tire has a fairly rough bead area, and not one that would naturally make a tight seal. But again, the sealant may make up for this to a degree.
As to the sidewalls, the likely problem would be that the tube-type tire's sidewalls are not flexible enough (and the bead not stiff enough), and so, when flexed, might not allow the bead to remain in tight contact with the rim. This could result in seal failures when hitting a bump, etc.