I know it's a little old, but I just wanted to weigh on this topic as I have only HD4600 in my current main (work) system, as I'm still not ready to go ahead and build my new gaming PC just yet.
Fallout 4 will run playably on this GPU, but as with other Bethesda games the main problem is the consistency of performance; Skyrim for example runs great on an HD4600 on even fairly high settings (no high-res texture packs though), but it will slow to a crawl under certain conditions thanks to unreasonably high resolution falling leaves and snow effects.
So my recommendation is to wait for more performance mods to appear on nexusmods.com, as these will help smooth out performance considerably. It still won't exactly be fast but personally I find 20-25fps more than playable in non-competitive games, and as long as that framerate is steady it won't get in the way of enjoying the gameplay.