I just ran MrDoob's FPS counter on Safari in a new Apple's iPad Pro (120Hz) but it only runs at 60fps, whereas a Chrome browser in a desktop monitor (with a refresh rate of 144Hz) runs up to 144fps.
The script uses requestAnimationFrame to calculate them, so it's not technically a resource-intensive consumption.
I couldn't find it on the WHATWG specification, but seems it should. References: