On the long run I think if Alice has spent 100 USD to buy some Hive and Bob has spent 100 USD to buy some HBD, both Alice and Bob should be treated equally.
Because HBD is just 'Hive But Disguised'
On the practical experience that should make Bob be able to stake his HBD in the same manner Alice can stake her Hive.
In other words to stake it for 13 weeks allowing Bob to take part in the reward distribution process.