Does the Auto 16:9 feature crop my recording?

No, content captured at a non-standard aspect ratio has letterboxing or pillarboxing added rather than being cropped.

If you record at a wider ratio, thin bars appear on the top and bottom to pad it to 16:9. If you record at a narrower ratio, bars are added to the sides. No part of your recorded screen is cut off in either case. The result is a correctly framed video that plays at standard widescreen dimensions without missing content.