From a pure technology perspective, you will be able to find quite a few different software options that can do basic facial recognition and photo comparisons. In this case, similar looking people may "matched". This is like the Facebook algorithm that tried to match names to photos of friends; however, these are highly flawed (e.g., a picture of my daughter always tags my wife).
Additionally, the level at which these types of software will operate will pale in comparison to forensic software, which is still not 100% accurate. NIST has evaluated algorithms that can obtain over 99.5% accuracy matching a person in multiple images; however, this is only under ideal conditions (such as using multiple high resolution photos of both subject and targets). But you have to note, these are designed to identify one person (not make a possible match between two people).
So while the historical background and speculation as to Lincoln's true birth parents may be interesting (we love genealogy and making these links after all), I think what you are trying to accomplish would probably result in even more speculation.
Also note, researchers who spend their life on this type of work will not even try facial recognition/matching in this situation...