If you have a G-sync display, it's doing it automatically at all times essentially. If not, it's possible to notice tearing or small stuttering as a result of the timings not lining up perfectly. I mean, if you notice them, you can go ahead and switch it, but Wolfenstein will give you that horseshit anyway, because both it and the original had serious frame issues of a few different kinds, even more noticeably so at >60FPS. Again, if you see something you feel is less smooth than it should be, you can go ahead and pull the display down to 60.
If your display has ultra low motion blur, you definitely don't want to be running content that's not the same as the display. I use a program called StrobeLight to force my display to do so (it was meant for glasses 3D, but this forces it on whenever you want. The result with the OS and nicely managed 120FPS content is ultra crisp motion, to the point were you can read small text flying across the screen insanely fast by tracking it with your eyes as it flies by. Without ULBM/LightBoost, it's literally just a completely unreadable blur, even at a perfect 144FPS. It's great, but the problem with games at 60FPS while in that mode, is that the clarity essentially accentuates the missing frames. Its like flashing a 1 on the screen twice in a row with large black portions in between, and then 2 twice the next time, rather than a standard display mode which would display 1 and hold it up on the screen, which then switches to two. Visually with numbers being a specific frame, _ being black screen, and - being a solid continuation of the frame, it looks like:
120 FPS 120Hz Screen, LightBoost OFF
1-2-3-4-5-6-
120FPS 120Hz Screen, Lightboost ON
12_3_4_5_6
60 FPS 120Hz Screen, LightBoost OFF
1---2---3---
60 FPS 120Hz Screen, LightBoost ON
11_2_2_3_3
I've also found that V-sync might not play nice. Adaptive V-sync does a pretty good job with 120FPS content on a 120Hz display, disabling when dipping below the refreshrate to prevent halving to 60, which standard V-sync absolutely does, thus causing huge stuttering. With BattleBlock Theater for example, a 2D game locked at 60FPS, the display doesn't auto switch to 60, and Adaptive V-sync outright does not work. It tears and stutters all over. Turning the display to 60Hz and forcing standard v-sync instead of adaptive in the Nvidia control panel, and it's fantastically smooth, for 60Hz anyway... Metal Gear Rising and Ground Zeroes behave the same, outright ignoring Adaptive V-sync entirely.
The Lightboost things can't really be fixed without display manufacturers developing a lightboost system that works at 60Hz, but basically all of the v-sync and stuttering issues I've described have all been fixed with G-sync. You've already purchased your display, but for everyone else, please don't underestimate the enormous benefits that come with variable refresh technologies. There are great options for both the red and green sides, and while they are expensive at the moment, they are coming down. But to be honest $700-800 isn't all that insane at all for 1440P 144Hz IPS G-sync panels we have now, compared to what we had only a few years ago.