It is perfectly possible to create a transaction that is valid but not broadcast to the Bitcoin network.
However the usefulness is a doubtful because what such a transaction will tell is basically "the person that created this transaction had control over this amount of money at this point of time", it has no use to actually transmit value as the blockchain does not timestamp the transaction by including it in a block and no one will acknowledge that the money has changed hands.
If you want to detail your use case you may get a better answer.