But what was his chances that he would be able to find it? He attacked "Enterprise" with such indiscriminate weapon as ramming drones. He could easily inflict such damage, that the ship would just disintegrate. Or, the crew may decide to activate self-destruct system. And after that, his chances to find the artefact would be null.
And again, such troubles only for a marginally powerfull bioweapon? Couldn't he just jury-rig a neutron bomb, or produce a few thousand tons of VX?
But he didn't inflict too much damage in the beginning. He boarded the Enterprise to get the artifact.
He saw the Federation and Starfleet personell as weak. I don't think he saw Starfleet personell as capable of self-destructing, self-sacrificing their ship and crew.
That bioweapon wouldn't have left a trace of the attackers. It would have put Starfleet and the Federation on edge. Probably produced another Admiral Marcus.