Mares begin lactation in the second half of their pregnancy this is usually the same time a mare may become immobile. Untill babbehs begin to drain the milk reserve production is limited to conserve resources. Lactation in the last week can result in dripping if the teats often rub on the ground.
Regardless of the amount produced mother’s are very protective of their milk unless otherwise trained.
His babbehs lives are at stake its not likely you will find another mare who doesnt have tummy babbehs who doesnt have some sort of Herd/Special freind to protect her.
He shouldnt give it a second thought, if this doesnt work you are gonna have to do it by force. survival of the fittest.