Can plants still absorb nutrients if they have become leafless?

Depending on how established it was and how big of a root system, maybe. If the fish already ate it all, they are likely to eat new leaf buds emerging.

That is the only plant I can't seem to grow in my tanks. My fish always devour it also, and it never recovers. I think it's the fine tender thin leaves, any fish that likes vegetation will eat it. Unless you are keeping just carnivore fish, IMO those things don't stand a chance.