Onions grown from seed produce a large bulb the first year.
That's how onions are produced commercially. Your onion shoot may well survive the winter and, if so, will produce an onion this summer. However, a lot depends on whether it is a variety suitable for a northern climate or is a southern variety. Onions are sensitive to day length and it depends on where your onion came from originally.
Good luck!

And, sad to say, in its 2nd year it will try its darndest to produce seed. Never the less, save the seed and plant it this fall or early spring and plant the little buggers when its time in your zone. You may get good onions or not. Depends a lot on whether its an open polinated varity or you may get lucky and end up with a new varity. Best of luck.

As an experiment, i trimmed about 1/4" off the ends of green onions and planted the; they are growing. Now depending on the variety; you might get a bulb, blooms or just another green onion (variety: bunching onion) Whatever the outcome; you are getting something for nothing but a bit of labor.

When I get a new allium, I isolate it in a pot where the runoff will not likely spread any infection. I watch the plant and have gone as far as to put the soil in my smoker to kill possible pathogens. That being said, I regularly get onions and shallots and garlic from retail and plant them. Often just out of curiosity to see what the plant does in it's full life cycle.