So... what exactly can you do with a stock PC from Walmart? This "beast" only has an AMD Quad-Core A6-7310 APU with integrated AMD Radeon R4 Graphics. At a whopping 2 GHz(2.4 boost) and a giant 2 MB cache, this core was paired with 8 GB of ddr3 memory and pretty much nothing else. Well, the answer might surprise you.
As seen in the above photo, playing CS:GO at minimum settings gives a playable 10-20FPS. Which surprisingly enough is good enough for those juicy frags.
As seen on the right, Gary's Mod runs at a very playable 40-60FPS.
On the other hand, you can see below that Besiege runs at a pitiful 5-15FPS, but really croaks with community creations, dropping all the way to 3FPS.
Other older games like Just Cause 2 and most Valve games run perfectly. Minecraft is a very playable experience as well, but it is a processor heavy game, so this is relatively predictable since the processor isn't that bad. I currently have two monitors plugged into this (using the VGA and HDMI) and I am able to watch YouTube videos on one while doing some light gaming on the other. Considering it doesn’t have a graphics card and is only using integrated graphics, it's pretty great if you think about it!
So, the answer to the question? My answer is yes, you can game without a graphics card. Just don’t expect to run any AAA games or other higher intensity games like Space Engineers or PUBG. But I still highly recommend building a gaming PC, you can spend about the same and still get a MUCH better PC. My PC is the HP Slimline Desktop 260-a059w which you can find here.