Does middle ear infection always cause drainage?

Not necessarily. The infection of middle ear would have to rupture the ear drum for a person to experience a discharge.

In decades of daily encounters with middle ear infections in birth to 21 yo, I would say that a few percent (1-2%) ever drain. Outer ear infections like swimmers' ear often do.

No, most middle ear infections do not cause drainage. An infection leading to a perforated eardrum could cause this; sometimes when the eardrum is inflamed the ear wax in the ear canal can get softer and drain; or a swimmer's ear (ear canal infection) can cause drainage.