For me the opposite is true, if they go the knee jerk approach and bring in any old manager or caretaker it would trigger alarm bells as it would demonstrate the same short-sighted approach we've had for a decade now, which is the primary reason we are where we are, miles behind the top teams.
A much better approach would be for them to spend a little time up until the summer in order to establish a style of football they want us to play, and find personnel (players, manager, coaches, etc) that fit, and bring them in early in the summer. A bit of planning will go a long way, we need to be able to think beyond a new manager bounce.