I do custom applications for a liquid handling robotics company.

Nucleotide extraction and amplification are some of the most common contemporary applications of modern liquid handling robots. Cherry-picking or sorting of samples is also a technique that is common and well within the functionaltiy of these robots.

To avoid cross-contamination, diagnostic samples are typically not mixed and handled in discrete wells with sample specific disposable pipette tips. In a scenario where throughput/cost/reagent scarcity are important and false-positives (without severe symptoms) are low-risk I think your suggestion absolutely has merit. I am going to run this by our diagnostics specialist for further review.