I've seen old 1960s machines with grease zerks and drain plugs and brand new machines with both. I've also seen tons of old and new motors with no drain or pressure relief plug that does have a zerk intended to be used to grease it. Rope sheaves can be found either way too.

If the manufacturer is still around I'd try reaching out to them just to check. But generally they designed it the way they did on purpose and the seal or shield on the bearing will let the excess expel out. I would just be cautious and use a little instead of alot.

Just as important as removing the drain or vent plug when there is one, is not mixing incompatible greases. I use a shearstable polyurea grease as it is compatible with pretty much everything (everything commonly sold that might have been used before). Its the green Lucas extended life grease, I have found its the best performing grease I've tried. Unless a specific grease is specified by the manufacturer.