I'm just not sure why anyone would want to do 15-20 minutes of pushups.
But yes, pre-exhaustion has been around for a long time. However, it was originally envishioned as a way to shorten a workout. Typically, you'd do one set to failure of an isolation exercise like, say, chest flies, then immediately follow with bench press.
It's obviously not a good strategy for increasing strength. It is, I suspect, good for hypertrophy.