4,000 sf is roughly 20/21 paces x 20/21 paces - a pretty small target for most golfers. I'll defer to Tom, All, Ian, etc. since this is what they're paid for, but perhaps if there are enough pinnable areas and more then ne ingress/egress for foot traffic to the putting surface AND there's enough natural light to maintain proper growing conditions, this would work.
My concern/issue would be more with the teeing ground for a hole with this sized green, especially if its a 1 shotter. A pet peeve of most of the anyone's customer base will the the conditions of the tees, greens/approaches then fairways, bunkers & then rough. Tees with little turf due to size limitations and overuse, soil compaction, inadequate sunlight, limiting teeing locations due to crowning from improper top dressing are all pet peeves of the customer base. I'd be hoping a 1 shotter with a 4,000 sf green has 5,000 sf of teeing ground, 3,750 sf of it for the daily tee placement.