No. Edgar is a spirit that inhabits the cows that enter the hole. As soon as a cow enters the hole it becomes Edgar. But when the cow leaves it becomes a random cow. Think of victor from fallout new vegas or agent smith from the matrix.
Edgar is the one in the hole. If a cow is in the hole, the cow is Edgar. If a skeleton is in the hole, the skeleton is Edgar. If a human were to fall in the hole, the human is Edgar.
Time does not exist in the hole. As such, it doesn't matter what they were before. They are Edgar now. They have always been Edgar. They will always be Edgar.
At least until they somehow exit the hole, at which point they cease their one-ness with Edgar and re-enter the speacetime of the normal dimension that cannot adequately contain Edgar. Thus the existence of the hole, which acts as a buffer between the normal world and Edgarspace. Edgar really is in there to protect everyone else. If Edgar were to exit the hole, the consequences would be disastrous. Catastrophic even.
So if one of the guys goes back into the hole for whatever reason, (be it another attempt to try to free what they perceive to be Edgar, or the result of a mere accidental fall) hope that the hole gets patched over quickly so that there's no risk of breaching the barrier between worlds.