I would say yes, but it would depend on workout design. I program intervals in Z2( mostly to break up the monotony), so if my HR is approaching the ceiling but I only have a few seconds left in my interval, then no. If I have longer time left in my intervals, then yes, I will drop my speed.
If I am doing straight time or distance work, then yes, I would drop the speed first, then, if needed, the incline, then, if needed, drop any weight I might be carrying to stay in my zone. A little bit of HR drift won't kill the overall benefit