Question

If cg adds it as a possible giveaway you can (i.e. there is an option to create a giveaway called "Bemine 3") so as of now that's a no. This would be for the entire giftable version of it

I don't believe you can make a Be Mine Bundle giveaway, as it is not listed under the create a giveaway tab. Also, you can't make individual giveaways for these games either, as it is against the Bundle's policy.