Yes. Recording and sharing are two separate switches on Daniel Newman Racing > Race Academy Settings, and the page is laid out to make the difference obvious.

Local data, stored on this PC:

• Record my laps on this PC, with an option to record every lap of the session rather than only your fastest
• Back up your laps to a file
• Restore my laps from the cloud
• Reset Race Academy data, which is permanent and cannot be undone

Shared data, your community laps:

• Share my laps online is the switch that publishes anything at all. Leave it off and your laps never leave your PC
• How you appear on lap boards controls the name other drivers see when they study your shared laps
• Remove my shared laps withdraws what you have already shared

So you can record everything locally, study your own laps, and share nothing. Turning sharing off later does not delete what you already shared, which is what Remove my shared laps is for.