Yep, that would work fine if you know ahead of time the shot was going to be that close. Things don't generally work that way. Like many of us, my shots range from 15 yards to 300 yards. It is the close ones that drive me crazy. That is why I am removing my 3-9 Nikon and mounting a 1.5 - 5 Leupold. It should increase my odds on the close ones without handicapping me much on the long shots.
Mounting one of the mini red dots (Burris, Doctor, etc.) on the top of your regular scope would be another alternative. The problem I think I would have with this kind of arrangement would be the drastic change in cheek weld required, and my probable lack of ability to make that change in the milliseconds required to make a fast moving, close-up shot at a coyote. Same would go for a side-mounted red dot.