My experience with this is that external deadlines work for teams that are unfocused and whose own motivation is low. However, for a team that is already executing well, an imposition of an external deadline (especially for a reason as poorly-thought-out as "to rally the team"), if it's aggressive enough to see increased throughput, will lead to poor processes, cut corners and burnout.
Perhaps there is an element of rationalization here, where a poor manager, who failed to anticipate at a distance a goal that was then attainable, becomes aware of it once it is closer and in danger of passing by, and has to make huge efforts at re-prioritization and motivation to meet it. In hindsight, the manager rationalizes that the fire drill was a good thing for the company, because obviously, the deadline was achieved! Oh, and look, next week there's a customer coming on-site, wouldn't it be great if this other feature was added in time for that...?
I have not had to build and lead a team yet myself, but the process I would follow, and the advice I would give others, is to choose to work with a focused, motivated team, and reduce the importance given to external deadlines. They should influence the prioritization given to relative projects, but cannot be used to crank the throughput nozzle.