Deleting a node just after it has been added I want to delete a node after it has been added (or modified), if certain conditions happen.

Is it possible to do that with hook_node_insert? (Considering hook_node_insert  will actually be executed just before the node is added to the database.)
I think Rules module will be helpful for you in this kind of scenario. Rules module help us to define actions on different events(like user creation, node creation/updation/deletion). It is a very powerful module.