Answer:
According to the phrase, it may seem that way, but actually, no, they do not.
The phrase "greenhouse gas" is simply a metaphor describing the ways bad air in the atmosphere can trap heat emanating from the earth just the way a greenhouse traps warmth for plants to grow. However, true greenhouse gasses do not help us grow at all--in fact, greenhouse gasses can, although indirectly, really have a serious effect on one's health. Acid rain and overly hot climate are just a few results.
Whether heat leaks out of greenhouses and actually does contribute to global warming, I simply do not know.