Does a database of IC chip Pin Outs exist that would allow you to find IC chips with certain pin outs or pin outs that match or nearly match other IC chips?
Would that even be feasible?
Yes, it used to be feasible. Sort of. Back when 14 and 16 pin TTL ICs were more or less standard, there were testers that you could plug unknown ICs into and it would attempt to identify them. But today there are so many different specialized and field programmable ICs and so many different families of ICs with different characteristics that it would most likely be impossible to account for all of them.
But if you're working strictly with ICs from the 1970s and 80s and early 90s, an IC Master is a good place to start. Even with one of those, there were so many specialized ICs made by Harris and other specialty manufacturers even then that it was sometimes impossible to identify even marked ICs.
In the old days you can use a Curve Tracer and other TE to determine which pins were power and ground and Input and Output with reasonably good results and then use a pattern generator and a logic analyzer to determine what the internal logic was. But once they started making ICs that used internal feedback to control the logic, that got very very difficult. And with PALs and GALs every circuit was custom and there were no more standard pinouts.
Back when manufacturers liked to grind the markings off of IC and then put house numbers on them, a couple of friends of mine had access to diamond slitting saws, microscopes and other high grade equipment and they would grind the tops off of ICs and read the OEM markings off of the die and could identify ICs that way. They then reattached the IC top. One even had access to a wire bonding machine and could replace burnt out bond wires. He told me that that was the most common failure mode in ICs in those days.