Yes, but that's essentially like hacking a CPM machine to emit a Microsoft Word macro virus. It's not that it wouldn't work, it's that it's a lot of extra effort for no particular reason except maybe bragging rights.

If the goal is to use a bio computer to compromise a biological system, a more likely pathway would be to get the programmable system to construct something more like a prion (an auto-catalyzing protein complex) rather than faffing about with all the extra complexity and layers of indirection of an infectious virus.

If your target bio system is a plant rather than an animal, constructing a viroid might be worth the effort.