Generally you want to have some kind of limit in place, yeah. If you don't, your GPU will just render as many frames as it can until it maxes out or something else bottlenecks it. OBS uses the GPU to composite scenes so if there aren't any resources left OBS performance will tank. Since one of Gsync's main benefits is maintaining smooth performance when your GPU can't hold the frame rate at your monitor's refresh rate, there's already going to be a problem if that feature is being utilized.
Best practice is to cap the frame rate at a value you know your GPU can maintain consistently without maxing out. If you want to take it a step further it should also be divisible by your streaming/recording frame rate. This value is going to differ between games so that's also something to take into account (e.g. you can hold 144 FPS in Minecraft easily but probably not in a CPU-heavy game like DX:HR or The Division without turning down some details).
There's a document around here somewhere with a longer explanation, I'll see if I can find it.
Edit:
https://gist.github.com/RytoEX/239f85c3515cae6b029bb909505a7333
This is a WIP document so the link may stop working or explode or what have you.