In conclusion, this scenario would be catastrophic and the methane wouldn't go away quickly either, since this would be likely to keep triggering further releases. While some models project rapid decay of the methane, those models often use global decay values and long periods, which is not applicable in case of such abrupt releases in the Arctic.
Instead, the methane is likely to stay active in the Arctic for many years at its highest warming potential, due to depletion of hydroxyl and oxygen, while the resulting summer warming (when the sun doesn't set) is likely to keep triggering further releases in the Arctic.
For more, see http://geo-engineering.blogspot.com