One of the things that usually happen when they push and push and push for some feature to get rolled out in the next quarter is that it often turns out to be a gigantic flop. Engineers are forced to spend hours they can't get back at the whim of management for something that was a complete and utter failure. I could imagine few things more demoralizing than this.

Agile is really meant to be about self organizing teams that take ownership of their own work and deliveries. The scrum master and product owner are just there to facilitate that.

When a team hits a blocker on a tight schedule -- particularly across third party teams, it's up to the management to figure out a solution -- even if it means gasp delaying the release by one sprint.