B.S.
I've read/heard sneaking out only makes things work. You need to make your goodbyes short and sweet. In time he will overcome the anxiety and learn you will be back. When little ones are little they have no concept of "mommy will be back later" They think when you leave your leaving for good. He just needs to grow up some more.
Perhaps you can get up earlier and then allow yourself some time with him right before you leave by eating breakfast with him or playing blocks (or other short game) with him. That may help also.