What if the ASIC found the solution, and then passed that solution on to the video card so that the video card can generate that necessary proof of work? In other words, couldn't they be made to work in tandem?
An ASIC does ONLY what the electronic paths in the silicon allow it to do. SHA256 hashing is what the ASIC in an ASIC miner does. If even one tiny little change to the computation is needed, that ASIC design is useless. Scrypt is way different from SHA256. There is no computation from any ASIC miner hardware that is even remotely useful in performing a Scrypt hash.