Both Blair and Paladin do refer to the Gen-Select as a bio-weapon in the closing scene, though. (Blair when he has to make the choice between confronting Tolwyn about the Gen-Select or the Dragons, and Paladin when he says Confed outlawed such things.) In universe, it does seem to be considered a bio-weapon.
As for whether the Gen-Select fits the *real life* definition of a bio-weapon or not, the biggest problem that we have is that we don't know exactly what a nano-bot is is made of (metal and silicon, or carbon/oxygen/nitrogen, the chemicals that make up biological tissue) and how it is made (is it created on some kind of incredibly miniaturised assembly line, or is it made inside a living cell, maybe using something like reverse transcriptase to create new bots the way a virus replicates itself?) I would probably go with the latter two options because the nano-bots replicate themselves inside cells. If that's true (and I stress if) then the nanobots would be made out the same materials biological organsims are made from, and made in the way that biological organisms like virus are made, which would put them with a reasonable of stretch of being considered biological.
Best, Raptor