Yes you can book a stay for them.

Yes you may get the points and credit and they may get any benefits you would.

But at some hotels will require you to come down to the desk before they release the credit and points and benefits, so you won't be able to get the points if they don't think you are there.

So in some places it may work, and in some places it won't.

Hilton doesn't care who pays for the room, it cares whose account the room is reserved in and who is actually staying in the room.