Yes, you will arrive a bit later. But not by much. Going with the example from above, a speed reduction from 75 to 60 mph for 10 miles of highway driving will have you get off the highway 2 minutes later. If that has you arrive late for work, just leave 2 minutes earlier. And yes, consequently, this will have you get up 2 min earlier as well.
But consider the following Extra bonus: Your chances of getting a speeding ticket or involved into an accident have gone down as well!