If my team hasn't killed Herald, can I still pick up the Eye?
No, you cannot pick up the Eye of the Herald if your team wasn't the team that killed the Rift Herald. But denying it is still good as they will only get the 200 experience and 25 gold for killing it and not be able to push your turrets with it. If no one steps on it, it will remain on the ground for 40 seconds before disappearing.
source- personal experience and testing with the training tool.