In Terminator The Sarah Conner Chronicles, we find out about an AI Chess computer invented by Andy Good. Did Myles Dyson use any of Andy's code when he invented the Neural Net CPU?
One of the things TSCC provided was that there isn't a single future; the future is always changing (and, in particular, Judgment Day keeps getting pushed back). See, for example, how in Terminator 2 Skynet was created by CyberDyne, while in T3 it was created by the US military.
So in short, after the events in TSCC The Turk became the basis of John Henry (and, to be fair, it's entirely possible John Henry might end up begetting Skynet), but until those events changed the future, The Turk may have been the basis for one alternate timeline's Skynet.
According to The Terminator Wiki, the Turk (and Turk 2) was the basis for the creation of another AI creation:
The Turk 2 was stolen and Andy Goode was killed. It was obtained by a man who sold it to the Zeira Corporation. The company started to do tests on the Turk, and eventually used it as the basis for John Henry.
However, Turk 2 has some traits (read programming) that may have made their way into Skynet:
Ironically, in trying to destroy the Turk, Sarah provoked the creation of the Turk 2, a more adaptable computer that was quicker on its feet. Andy describes the Turk 2 in a way that could also apply to Skynet and the terminator AI: having a hunger for learning but not always learning the right lessons.
I don't think there was ever a direct answer to that particular question, though Andy Goode worked as an intern for Miles Dyson at Cyberdyne. It's more likely (given Miles experience) that Andy used what he learned from Miles in creating the Turk, rather than Miles using Andy's code in the Neural Net CPU.
EDIT: The timeline presented in TSCC provides that the Turk eventually came to become John Henry ("good" Skynet), and that there is still some other version of Skynet out there ("bad" Skynet) that sabotaged John Henry. That particular AI was associated with the Kaliba group, which many have theorized to be the TSCC-timeline version of Cyber Research System (the company that worked with either the US Department of Defense or the US Air Force to complete work on Skynet, depending on which timeline you look at). Most likely, despite Sarah Connor's efforts, the TSCC hostile Skynet is operational due to Miles Dyson's work on the Neural Net CPU, rather than Andy Goode's work on the Turk. I am only referring to the timeline presented at the end of TSCC; there were timelines where Andy Goode was responsible for Skynet, but not the last one presented.