That is correct if the lens is in factory condition. In reality many photographers took out the "rabbit ears", rendering them unusable for open-aperture metering on Non-Ai bodies.All AI lenses had the meter coupling shoe that all F2 metering prisms require, so all AI lenses would work with all F2 metering prisms.
The OP stated that his Nikkor has the inscription "Nikkor-H". That can only be a Non-Ai lens, albeit it could be Ai'd, which means converted to Ai standard.
Nikon changed the lens designation before changing the mount. The Nikkor-H 50mm became simply the Nikkor 50mm with a rubberised focusing ring and still as a Non-Ai lens.
The Nikon F2A and subsequent models had an Ai prism. If the lens isn't an Ai, it can only meter at working aperture.