Do these hammers raise the current durability of an item as well?

Yes, it will raise both max and current durability together, at the same time.

@Yinato, read the description.

I read the description, but of the 3 times I've used those things (most recent being shortly after the anime event), the current durability wouldn't change.

I don't remember current durability going up either when I used them... unless I'm thinking of golden hammers.

I distinctly remember Edern derping a repair right after I used one on my HLB (and it was at full dur before I used the platinum hammer on it).