If you turned on V-Sync, then yes.Eg. At 4K, the TV functions at 30hz, and is therefore capped at 30FPS, whereas at 1080p, it functions at 60hz and may be limited to (up to) 60FPS?
Anyway, if your TV can only display 30FPS. Then let the GPU deliver 30FPS is the way to good. Let the GPU work at 60FPS, but half of the frames never display is meaningless. It's just a waste of energy. Let the GPU work harder / hotter for nothing.