Whether Congress passes an AUMF or does not pass an AUMF, it’s not going to affect an iota of activities on the ground.
Whether he meant to or not, Corker has succinctly summed up why the entire debate over a new AUMF has been so absurd. If Congress authorizes the war, the war will continue, and if it doesn’t vote on an authorization the war will continue. All indications are that if Congress voted explicitly against authorizing the war, the war would also continue. In that sense, Corker is absolutely right that it will have no effect. Corker is drawing attention to the reality that the U.S. will keep waging the war on the president’s orders no matter what Congress does regarding a new authorization resolution. Most hawks think this is just fine, which is why they feel no need to make an issue out of this, and they happen to be the ones in charge of both chambers.
Unless they are prepared to vote against the war and cut off funding for the war (and they aren’t), Congress has for all practical purposes been left with the choice between formally endorsing Obama’s war and letting it continue without comment. Corker is admitting that the president will not be bound in practice by any limitations contained in a new resolution, which is clearly true, and so he sees no point in going through the motions of crafting and passing one that the administration will ignore or distort beyond recognition whenever it wishes. Under the circumstances, it probably is better that there isn’t a specific authorization for this war, since that will deprive it of the veneer of legitimacy that will help to keep it going longer. As it is, the U.S. should be looking for a way to get out of the war  instead of worrying about getting Congress to rubber stamp another unnecessary intervention.