If I manually flag a group of IPs on a trial account in the Sandbox environment, will they be flagged in the whole system and when the system goes live?

Sandbox and Production are two separate instances. However, due to how the Flags work as a shared attribute across all SEON accounts (if they opt in), when you flag something in Sandbox, the flagged information would be available in Production as well. You can read more about the flagging feature here.