You will need to have a connection to a node to deploy your smart contract, but this does not mean that you need to run your own node. You can choose to use a 3rd party ETH node service such as Alchemy or Infura with Truffle or your own ETH node. See this document on how to change your ETH node connection in Truffle. You will need to set your deployment parameters on Truffle to the corresponding node provider that you are using.
Once you have deployed your smart contract, you do not need to run a node to serve this smart contract. The smart contract has been deployed to the Ethereum network and will be added to the state of all other nodes in the Ethereum ecosystem.