I thought there was an external solution.
Agreed, by the time you've done all that you could've just spent $500-600 and bought/built a mid-range PC.
^ what Spikes said.The Intel UHD graphics won't run AH, it may even start to a white screen only as has been reported several times during the history of AH3. The Dell Hazmatt suggested is not much better, further it's not a mini-pc by no means. Searching for "mini gaming pc" on Amazon shows a bunch of tiny boxes featuring strange names and one that certainly would run AH quite well: https://www.amazon.com/GeForce-Graphics-Lighting-Vertical-Included/dp/B0DK86TS91. Even that would be twice the size of the mini-pc mentioned by the OP.
Interesting theory. I have no idea. We use a mini at work for co-workers to access payroll information. I think they are kind of cool.