As soon as a node creates a transaction, that transaction is propagated across the network, even before it is confirmed/mined in a block. So this would only be an issue if the node stops in the split second between the new transaction entering the local memory pool, and it propagating to other nodes' memory pools.
Transactions are also stored locally on disk at the moment of creation, even before they are propagated, and will be reloaded from this store when the node restarts. However for performance reasons this on-disk storage is not flushed after every transaction, so if there's an OS-level issue (e.g. a power cut) it could still be lost.