replace by fee – Does `0 OP_CSV` force the spending transaction to signal BIP125 replacability?

If I send bitcoins to an output whose script will execute 0 OP_CHECKSEQUENCEVERIFY when it is spent, does that require the spender to set the BIP125 signal indicating that the transaction is replacable?

For example, in cases where participants in a contract protocol (like Lightning Network) wanted to ensure a transaction would signal it was replacable, could adding 0 OP_CSV to all script branches provide that guarantee of replacability?

Additionally, would 0 OP_CSV impose any additional requirements on the transaction executing that operation beyond it needing to signal replacability and having a transaction version number greater than 1?