My experience is that increasing resolution puts more load on the videocard. It does not help the CPU because the CPU will be doing the same amount of work no matter what the resolution.
Your friend's problem is likely this: At ultra or max settings certain options, like view distance, are CPU dependent as well as videocard dependent. He has a dual core with hyperthreading, not a quad core. So in some games ultra settings are too much for that CPU even at lower resolutions than the videocard can handle because the videocard is not the only thing determining how the game performs with that setting.
edit: So no, getting a 1440p monitor won't help, it'll just put more load on the videocard and lower overall average framerate.