Most likely the plants would shut down, the major issue for many turbines is the fact that they have hydrogen in the generators to cool them off and require seal oil to keep the hydrogen in there away from anything else (especially oxygen). If the transmission line goes and there is no power backfed to the plant the seal oil pumps will shut off, the hydrogen will then escape the generator and mix with oxygen causing an explosion that will basically destroy the generator itself.

Most gas plants require hydrogen to cool their generators, if the supply of hydrogen runs out then the plants shut down automatically, or worse. Typically hydrogen is provided in a trailer that is dropped off every couple weeks. Speaking from experience a plant that runs on a hydrogen trailer would probably shut down in 2 days if nobody was around to put new hydrogen cylinders into service.