I am curious if it's possible to beat ToA Adventure Mode (A Demon King Victory Screen being the end goal) with only 1 in each stat. Part of me thinks no, mainly because you won't earn any Soul Crystals if your Magic Level isn't high enough (unless that got changed), you wouldn't be able to upgrade your gear to compensate. (Plus end-game gear weight would cause massive penalties)
Another issue is the lack of Magic, Perception & Charisma potions, so you can't simply buff up to bypass the CHA skips for some encounters. You can however use Agility Potions to do some Agility Checks, so that's at least one potential issue solved. Another big key hurdle would be Dark Knight, since you won't have Parry + Trip or any significant dodge moves (I believe Leg Sweep has been either massively nerfed or it's currently not working if your speed is too high)
Can't slut it up too much, but Lewd Energy would be a good way to deal with certain enemies. Alternatively, you can use the Outpost Bonus Purchase to bypass the first Dark Knight fight and then just grind in the Waking Lands (however you wouldn't have any way to spend gold for items so you'd be stuck with starting gear).
TL;DR A Stat 1 run might be possible, since with high enough Skill Points + Perks in certain things you can bypass a lot of checks. A hypothetical that's interesting, but I pity the person that tries.