Yes its possible I am using a Intel HD 4000 And have been able to set a 4k display at 24hz (the refresh rate is limited by the pixelclcok on the on-board GPU This is without any overclocking done to the graphics card.
Now I can play games on it fine because the TV has a post processing and I do not play fast twitch games (I mainly play Eve online) this is also assisted by a dedicated PhysX processor (the GeForce GT 630M to be precise)
TRY THE BELOW SETTINGS AT YOUR OWN RISK I AM NOT RESPONSIBLE FOR ANY DAMAGE TO YOUR SYSTEM
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the settings I've used are below:
SYSTEM INFO:
Intel(R) HD Graphics 4000
Report Date: 9/3/2015 Report Time[hh:mm:ss]: 05:41:14 Driver Version: 8.15.10.2752 Operating System: Windows 7 Service Pack 1(6.1.7601) Default Language: English (Australia) DirectX* Version: 11.0 Physical Memory: 16271 MB Minimum Graphics Memory: 64 MB Maximum Graphics Memory: 1696 MB Graphics Memory in Use: 1212 MB Processor: Intel64 Family 6 Model 58 Stepping 9 Processor Speed: 2294 MHz Vendor ID: 8086 Device ID: 0166 Device Revision: 09
Processor Graphics Information *
Processor Graphics in Use: Intel(R) HD Graphics 4000 Video BIOS: 2137.0
4K plays just fine on a trinity apu. I'd reference a video or two but can't find one on youtube at the moment that mentioned it. I think either @wendell or linus or someone mentioned something to that affect.
Would love to see what 4K looks like myself but my laptop doesn't even know what 4k even is...
I get 4k at 24 HZ thats limited by the 4000s GPU pizel clock frequency of 220 (the scan rate is set at 24 vertical) i can push to 25/26 HZ but its not much better as the post processing on my tv has issues at those unusual frequencies.
But that is just the refresh rate of the screen, no? I was wondering how well a game would play at that resolution (since it seems you play at least something on it).
I have no issues with the games usually the games out perform the monitor i get 30-60 FPS (on the games) dependent on if we are talking static images or high depth images.
but as the display is the weak link i gave you the "weakest link" frequency refresh rate.