I have a Private Ethereum Network. As a node I connected to the network as a peer. When I submit a transaction from my node, it won't fall into mining pool, in case I start mining on my node.
When I start mining on my node, the transaction get eventually mined.
The transaction that has deployed the contract needs to be verified by the network, if we are running a private chain with a single node we will need to mine the transaction. 
[Q] If we are running a private chain with multiple nodes as a connected node still do I need to mine the transaction? As I understand each node is forced to do mining for their transactions to get into mining pool. Is there any way to push my transactions into mining pool without start mining?
Thank you for your valuable time and help.