Methane is a quite potent climate gas. But it acts only during a short time.
The lifetime of methane in the atmosphere is relatively short, ~9 to 10 years at present. (Brook, E. J., Sowers, T., & Orchardo, J. (1996). Rapid Variations in Atmospheric Methane Concentration During the Past 110,000 Years. Science, 273(5278), 1087–1091. doi:10.1126/science.273.5278.1087)
So, if there are large methane sources in the permafrost which will be released into the atmosphere if the temperature increases, this will be a short term problem. The temperature increases for ten years, and then decreases again, if there will be no more supply of new methane. But if a certain amount of permafrost is no longer permafrost and its methane content is in the atmosphere, then this part of the former permafrost is no longer a problem at all.
It is, nonetheless, not completely harmless - it may increase the speed of a warming. But it does not increase the final temperature.
What would influence the climate in a long range would be modifications of permanent sources of methane.