Well no.
https://nsidc.org/cryosphere/frozenground/methane.htmlThe total atmospheric carbon is 850 gigatons. The permafrost has another 1400 gigatons. So all the permafrost would triple the total amount of CO
2 in the air. Which is bad, but let's compare that to
Venus.
Earth's atmospheric density at sea level is 1.2 kg/m
3, while Venus's atmospheric density is 67 kg/m
3, which is 5583% of the Earth's atmosphere.
Venus' atmosphere is 96% made up of CO
2, while CO
2 makes up 0.04% of Earth's atmosphere, and after releasing all the permafrost carbon, that would be 0.12% - a rise in Earth's atmospheric density of 0.08%. So the increase in density due to the permafrost carbon would be too small by a factor of ~70000 to give us the same atmospheric density as Venus.
Clearly, the only way that the atmospheric density can reasonably rise is because the oceans get heated by all that CO
2 and start evaporating and bloat the air with water vapor. Water vapor
absorbs heat so it's greenhouse gas. However it's also reflective and creates clouds, reflecting sunlight away. So a Venus-like atmosphere made of mostly
water would have entirely different thermal properties to the actual Venusian CO
2 atmosphere.
As an aside, let's see if there's enough water for that scenario.
Earth atmosphere weighs 5.15×10
18 kg, and we already worked out that the density is 55.83 times less than Venus. So we need 2.875245 x 10^20 kg of water to make a Venus-thick atmosphere. "The total mass of the hydrosphere is about 1.4 quintillion metric tons" which is 1.4 x 10^18 tons, or 1.4 x 10^21 kg. So yeah, if 20% of all the water on Earth evaporates, we
could have a venus-thick atmosphere. That's not very likely however. And the stuff is very reflective, meaning it'll stop the sunlight getting to the surface. CO
2 works differently, I believe (not 100% sure, a science buff can correct me if I have this wrong) that it lets more sunlight frequencies through, but blocks infra-red wavelengths, meaning it lets energy in, but not out. Water vapour however doesn't work like that.