So, curiosity got the better of me and I wanted to see just what kind of performance hit we'd be looking at.
I have an old HP 8200 with an i5-2500. It has decently better single core performance than the J4105 (1706 vs 1092), but the next step down I have is a C2D E6400 which is decently lower at 824 ST.
Installed a Quadro K2200, which is basically a 4GB version of the GTX 750Ti. I ran Passmark GPU tests, and got 3777 G3Dmarks at 33W peak(via HWinfo), which is pretty inline with what you'd expect.
I then tossed it on a x1 riser card like you'd use for GPU mining, and it ran at PCIe 2.0 x1 (5GT/s). Ran the benchmarks again, and got 2008 G3Dmarks, with an peak power draw of 30.7W.
I don't have a ton of other low power cards to test, but that's probably a best case scenario since 4GB is a pretty large buffer in that performance class.
I adore jank so I definitely won't tell you to stop. If you're out shopping cards though, I wouldn't spend much there as running it from the Wifi m.2 is a real limitation. 1030 if you can get it for cheap is a little less powerful than a 750 Ti and quite efficient. 750 Ti if cheap is a Maxwell part with a better NVENC than Kepler if that matters to you. No H265 though which the 1030 would have (as would the GPU on the J4105).