If the user installs from an SKAdNetwork campaign, will the Branch SDK still send events to Branch in parallel to sending conversions to Apple? Will that data be ‘organic’ in analytics and exports?

If you are tracking events with the Branch SDK, it will continue to send events as it does today. However, those events will only be attributed to the ad touchpoint if the user opts into tracking. See this FAQ item for more details: What happens after users opt in via the AppTrackingTransparency modal?

SKAdNetwork provides a completely separate, far more limited dataset. Branch provides a tool to map existing Branch events to SKAdNetwork conversion-values but these events will not be merged together inside the Branch dashboard.