Can a subscriber be a publisher at same time
Yes, you can achieve the goal and implement replication topology. What I understood from your requirements is depicted in the diagram.



To do this follow these steps:  


Enable distribution on Server 1.
Create replication, add articles and choose server 1 as publisher and server 2 as subscriber.
Once articles are replicated, enable distribution on server 2.
Follow step 2 for servers 2 and 3.