Can a dual occupancy be built on a battle-axe block?

Yes. A dual occupancy can be designed on a battle-axe block, subject to meeting the applicable planning requirements.

The ACT Missing Middle Housing Design Guide specifically provides an example of a dual occupancy on a battle-axe block. In the example, the block also fronts public open space, and the dwellings are positioned to provide front gardens and direct access to the public open space, supporting activation and passive surveillance

Whether a particular battle-axe block can accommodate a dual occupancy will still depend on the site's circumstances and compliance with the applicable Territory Plan requirements.

Reference: ACT Missing Middle Housing Design Guide – Site and Land Use → Irregular Blocks - https://www.planning.act.gov.au/__data/assets/pdf_file/0020/3092411/ACT-Missing-Middle-Housing-Design-Guide.pdf