Not until the path deviation limit indicators on the PFD turn amber will thrust then increase, and then....mode switches back to VNAV PATH and aircraft will attempt to rejoin the path with A/T thrust at the SPD INTV speed (300).
That's not how the system works. If you enter SPD via the SPD INT, it doesn't attempt to recapture the path. It'll honor altitude restrictions, but not path.
Like Skyjob said, that's where the FMC DESC SPD is a better option.
(Assuming IDLE DESC option.)