If methane in the water effected the ability for ships to float, the ships working on the BP oil spill in 2010 would have sunk. Much of the flow from that well, was methane. The hydrocarbon plumes that concerned some, turned out to be all methane. What was learned was that there are natural bacteria in the Gulf that enjoys eating methane. Their reaction was fast enough that some researchers now feel that any 'eruption' or thawing of the methane clathrates would not cause a major climate issue since the bacteria would eat it first
It did sink, BUT it looked like to me that they HAD arrange it so it would sink. That was a LOT of weight in small open boat, and it appears to me that it didn't sink from a change in the buoyancy of the water, but from all the water it took on.
Doing a little more reading, it looks like it is possible, but very improbable.
An open-hulled outboard motor boat is not designed like a ship. Ships are designed and operated to have decks awash with no problems, they aren't motor boats with open hulls ready to fill up with water like the motor boat experiment.
If methane eruptions were causing ships to go down, at least one of them would have escaped to tell the story.
As a merchant mariner, I've never heard of such an occurrance.
I've seen swamp gas seeps offshore, and in the swamp. Most of these are decaying plant matter, biogenic methane, not prehistoric natural gas methane.