We buy scallions from the market and consume everything but the bottom parts of the plant (I guess it's like white bulb part?).
Is there a chance that it will still grow even after refrigeration? The scallions have small roots.
Oh yes, they will. I always do this and one or two bunches from the store is enough to produce green onions for an average household for a few months. While the scallions are refrigerated in the store, I try to chop off the bulbs as soon as I get home and plant them. However, a day or two's delay shouldn't matter. Onions are generally very easy to grow (probably harder to get the perfect onion).
I normally plant them in 2 groups. The first is in bunches of 6, so that the bulbs are really crammed below and don't grow much. This makes the leaves stay young and tender for longer (I don't have anything to back this claim... just what I've observed), and I regularly harvest them for my salads/soups/noodles, etc. Harvesting the leaves regularly also means that they never go to flower (bolt). However, the yield decreases after a few months and at this point, I just grow another set of bulbs from the store and once they're ready, throw these out. Repeat cycle.
The second group is in bunches of 4 like in the picture below (I parted the soil a little to show the bulbs). This way, they have enough room to grow into little shallot sized onions (these are not exactly shallots, although I use them as substitutes) yet not enough to become full sized onions. However, the leaves in this case (because I don't harvest them) are longer, stiffer and more mature than the first case and not exactly suited for recipes where you just sprinkle chopped green onions in the end (effectively being raw). In dishes where it is cooked, it tastes perfectly fine.
I had a friend tell me that I could put about the last 2 inches of green onions in a shot glass or other small glass, fill it with water (being sure to leave to top sticking out), then stick it in my window sill so it gets a lot of sun, and they will re-grow! You just have to keep an eye on the amount of water so it doesn't dry up. I've been doing it for the last couple of weeks and I have about 12 growing. Some are already ready to use!