If an admin partially blocks a user from Property:P18, currently they wont be able to edit the claims on that property. However, they will be able to to use the property. For instance if they want to edit the image (Property:P18) statement on Q4757092 they would be able to do so.

Should partially blocking a Property also block usage of that property?

The way this would work, is if you go to add/edit/remove a claim, Wikibase would execute User::isBlockedFrom on the entity they are trying to edit (Q4757092) as well as the property of the claim they are trying to edit (Property:P18). They must not be blocked from either one in order to make the edit.