No, it is not necessary to implement the AppTrackingTransparency prompt in order to use Branch: there are many valid Branch use cases that do not fall within the scope of Apple's policies on 'tracking', including deep linking and measurement of owned/organic channels.
For more information, please see these FAQ items:
What counts as an 'ad' and 'tracking' under Apple's policy language?
Are organic/earned channels under the scope of Apple's new policy?
If you choose to show the ATT modal, you will simply continue receive device-level data from Branch for ad conversions when the user opts in on both ends.