Need a bit more details about your plans, a NAS is simply Network Attached Storage, you can set that up in many ways. If you don't format the drives you won't lose any data. To avoid data loss you make backups. If you don't have backups of your files, do that now.
You can share out those drives using a computer, plug them into a router with USB ports for storage. Removing the disks from the enclosures is riskier since many external drives depend on the electronics to run properly, some for encryption, some for working the the large disk sizes, some due to custom SATA connections on the board, etc...