What I have heard is mostly anecdotal. But consider... the Pacific is a giant nursery for millions of tons of vegetation. When that vegetation dies & sinks it's subject to anaerobic decomposition which yields large amounts of methane. Those plants that are eaten by fish yield manure that also decomposes yielding methane. Granted most of that methane is trapped in complex hydrates but common sense will show a percentage of that methane will be released. Truthfully the point is moot as the process has been going on since life developed in the oceans and would have been present during glaciation as well the carboniferous period.
I will look into this more. But from what I recall on cattle and the methane they produce, I seem to remember that by volume, methane is far less efficient at blocking heat radiation than carbon dioxide. If that is correct, I can understand how large volumes of methane may not have as great an effect as smaller volumes of CO2.
As you say, if it's been happening for millions of years (which it surely must have been), I would say the effects are accounted for. I'm sure climate scientists are aware of it, and are probably measuring it in some way. Just like they're measuring all sorts of other potentially influential factors.