Modern ones will. The gpu requirement is basically says any gpu from 2011 and newer (2011 was gcn 1.0 and kepler) with Vulkan support.
For windows, vulkan is supported by skylake(6th gen) and newer, for linux, vulkan is supported all the way back to Ivy Bridge, but the experience playing CSGO would probably be terrible.
Thr 7840U is core config wise, the same as the Asus ROG Ally with the Z1 Extreme, just different clocks/binning. (Handhelds are drsigned for 10w handheld use, and 15-30w docked)
The 7840u is designed for 15-30w, but is meant for the 30w usecase. Other chinese pc handhelds like the Ayaneo Air 1s or the GPD Win 4 Pro already use the 7840u im their designs.
Its not that its bad, but usually its extra steps.
Most games. In particular ones running directx, use xinput, microsofts input library, which basically maps out to a generic 360 controller.
Controllers that arent designed explicitly for xinput use (many 3rd party controllers do, in particular one designed with pc in mind, but not all) like nintendo and sony controllers (for obvious reasons) use the legacy dinput communication, which not all games support.
Generally you can get around this via steam big picture mode, which uses steams controller API to map Dinput to Xinput automatically, else you have yo use 3rd party software for full compatibility (e.g ds4windows, dll mods) if the game or application does not natively support dinput.
The best situation would be of course, just plug and play, and open up all features of a controller to thr computer, bonus points if it changes the on screen input commands to the controller youre using (some pc games already do that natively)
Its just a matter of getting a invite code from someone whose already in the door. There is basically lots of people who generate it for others. Id do it if I was at home.