Asics, perhaps not.. yet.
But I have been thinking about something similar for all those GPU mining rigs people have stashed in their closets, I mean lets face it -- alt coins introduced a ton of GPU miners early last year.
That said, there is some potential here when you look at some Deep Learning java code, that *already* runs on GPUs... If the next few weeks permit, I might make fork a coin project locally to test how a split of work would be achievable. The main issue I see with this is extending one of the miner programs (cgminer,sgminer,etc) to achieve this double work (Where something like half of cycles run the deep learning code, the other half run the network)
For reference,
https://github.com/ivan-vasilev/neuralnetworkshttps://github.com/SkymindIO/nd4j