I would like to know if turning on FileVault affects TimeMachine Backups; if yes how?
(E.G. Do the backups become encrypted? etc.)
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Time Machine makes a second copy of your data and operates above the Core Storage layer.
File Vault is simply Core Storage setting a scrambling / encryption of all data before it gets written and after it gets read from one or more physical drive(s).
Combined, you can have FV on your real data and not on your TM data. Or the opposite. Or both or none. It all depends how you set it up as nothing changes automatically and you have to manually choose / set-up File Vault for each volume/drive where you wish to have data protected.
In the case you propose (turning on FV on source data), this won't change the encryption on/off status for an existing Time Machine destination. The only way the backup data gets encrypted is if you enable that on the drive when prompted or by intention using Disk Utility.