There is one method you can use but it is a completely manual process. Open the block schematic from the 'Blocks' node and assign reference designators manually using the 'Add properties' dialog. Ensure you assign these at the 'Block level' not 'Instance level'. When you cut and paste this block the reference designators should now copy with the block (cut & paste). However, any changes you make in PCB, such as pin swaps or gate swaps for these parts will probably cause the reference designators to get overwritten at the instance level.