The village where I've lived for the last 14 years has had a number of foreign Chairmen of the HOA. I know them all well and none of them has ever had a work permit simply to act as Chairman of the HOA.
One of them, though, did like to do various jobs around the village himself, partly for exercise, but he was advised by several owners and, I think, the Juristic Person, that he should not do things like painting or gardening in the public spaces as they do require a work permit.