I don't understand your skepticism, if a deadline is in a contract, and the company is not heading towards meeting that deadline, someone has to speed up or else the client will be lost, or worse the penalty clauses will kick in. I think you're imagining B2C SAAS startups when making that assertion.
If your EULA indemnifies you from failure to provide service, and investor capital indemnifies you from failure to get revenue, then yeah it doesn't really matter what the engineers do - but that's hardly a universal principle of business.
Overworking people dont get you faster releases. It is magical thinking. This just feel good like doing something, but that is is.
Also, if you are really in this situation, you already lost, because mo way this late night code wont be complete crap. So you might just start prioritizing and negotiating now rather then later.
If your EULA indemnifies you from failure to provide service, and investor capital indemnifies you from failure to get revenue, then yeah it doesn't really matter what the engineers do - but that's hardly a universal principle of business.