Ummm... not so.
I tried it. I chopped my green onions off, stuck the bulbs in a jelly jar and kept them watered on my kitchen window sill. Sure enough within in a few days they were HUGE. I was regretting the two rows of onions I planted in the garden and religiously watered for weeks by hand until the irrigation water was available.
I trimmed my forever green onions back again and waited. It took about a week and half this time, but they did grow back. Pretty neat.
The third time was NOT the charm. I needed some more green onions for my yummy taquitos so I trimmed them a third time.
It's been 3 weeks since they had their last hair cut. They've gotten thinner and aren't coming back so well, the poor things. I think I might find some room in my garden for the little guys to get their strength back. Guess my 5th grade science teacher was right. Plants need water, air, AND soil to grow.
They aren't forever onions, but one bunch stretched to 3, so it did save money.