From the very same wikipedia article you referenced, under "Current Outlook":

Most deposits of methane clathrate are in sediments too deep to respond rapidly, and modelling by Archer (2007) suggests the methane forcing should remain a minor component of the overall greenhouse effect.[28] Clathrate deposits destabilize from the deepest part of their stability zone, which is typically hundreds of metres below the seabed. A sustained increase in sea temperature will warm its way through the sediment eventually, and cause the shallowest, most marginal clathrate to start to break down; but it will typically take on the order of a thousand years or more for the temperature signal to get through.