One of the key aspects of ASMR is that it is a very relaxing state which seems to de-stress the mind and body.
Exercise is basically the opposite. It is a high energy state of physical exertion and mental alertness which stresses the mind and body.
Combining a stress state and a relaxation state to alleviate depression may seem a bit counterintuitive, but a study recently published in Translational Psychiatry (a Nature journal) has some interesting results.