Good topic. I don't exactly do hill sprints, but I do use hills in a strategic way when I'm pointing towards races. Just this morning, halfway through a "season" that has seen me run three 5Ks and one 8-miler and will have me running another three 5Ks and a 10K peak race before it's over, I did a run I haven't gone near in a couple of years. I warm up for 3-5 miles, then run 3 x 60 sec steep hills. I don't have to spring, just get up on the balls of my feet, keep cadence reasonably high, and push through to the top. The whole point of the workout is quad strength. I get to 95% of HR max by the last 15 seconds, but it's not training my CV system in any traditional way. The point is, by the time I do the hills, including, at much lower HR, some uphills and downhills in the warmup portion, I've run 6.3 miles with 500+ feet of vertical. 
It's quite possible to do some "hilly" runs of 8 miles with half that much vertical--I've got a doozy that I run regularly--and build some strength. But nothing quite matches the training effect, the bang-for-the-buck effect, of those 60 second steep hills. They quickly help you realize that you've been ignoring a key component of training. When I was younger (I'm 67) and in better shape, I'd do this morning's run as 8+ miles with two sets of 3 x 60 sec steep hills. That was a killer. You just catch your breath at the top, jog slowly down to the bottom, pause briefly, then do it again. A humbling workout. The point is to do it often enough--four or five times--so that it no longer humbles you. 
You were asking, though, about periodization: when to do this. Normally I would have started hills earlier, but as I age, and as the Mississippi summers feel hotter, I just can't stomach the hills until it cools down. Hell, I used to run 10 miles midweek--4 miles out to Thacker Mountain, then 3 x 4:00 up the mountain, then run home at threshold pace. Those longer hills, done at threshold pace, with a sprint in the last 30 seconds, build incredible strength. (The Kenyan way, LOL.)