How would the PC be used? I'd say it's a stretch, but it should work as long as you're conscious of the risk involved. The ripple/noise spec of that unit is right on the ATX spec (120mV p-p), but according to the test report real-world ripple is below 50mV p-p, which is perfectly fine. With a 65W max output you'd need to be very careful of the parts you put into this build - a 35W APU can spike up higher during short loads, and at this level every watt from other components will count. If you go for 1.2V DDR4, a low-power SSD (not a high-end NVMe drive) and nothing else you ought to be fine. 35W from the APU + 5-ish from an SSD and around 10 from the RAM and motherboard places you at 50W, but that number assumes that all these will be consuming their full power at all times, which isn't really the case. But again, the APU might spike noticeably higher. BIOS power limits would definitely be worth looking into.Do you experts think the Meanwell EPS-65S-12 would be suitable for an APU build (e.g. Athlon 200GE-based)? This thing is even smaller than the EPP/RPS 100 and 200 Watt models!
I've got an Intel J1900 board (10W, mind you, not 35) that I've run off a 12V3A (36W) power brick from an external 3.5" HDD - so it's definitely possible with the right hardware. If I was you, I'd give it a try while constantly monitoring system power draw with a kill-a-watt-style power meter, and declare it okay if total system power under a heavy load stays below 60. Remember that whole-system power includes PSU efficiency losses, which with the EPS-65S-12 should be about 12% - so a 60W reading for the whole system places system power draw at around 54W or slightly below. If the system pulls that much under a steady load, I don't think I would quite trust it, but if total system power is at 50 or so, it'll probably be fine for a few years.