Does this mean that the Dac is immune to noise/jitter generated by a computer usb port connected to it?No. No such thing as immune.
And will a special noise isolating USB cable be required in this instance?No. No such thing as required.
I've seen a lot of threads touting audiophile usb cables and at present I'm not using one.
"Touting" is close to being right. If touting you mean a story like galvanized this, jitter that. Then yes that is a tout. But if by "touting" you mean people reporting big improvements in sound quality no that is not a tout that is the impression of a listener. Someone actually tried it and heard it was better. That is not a tout. That is an observation.
The key to your situation is you are now using very ordinary wire. Just possibly maybe one tiny little baby step up from the freebie junk that comes with whatever you bought. That being the case, almost any of the better wires you are looking at will be so much better it will be easy to hear and appreciate.
Where it gets interesting is once you do upgrade, to find out just how much better a wire can be. Right now starting from zero everything will be amazing. Once you upgrade the improvement with even better wire is still there, only you find more refinement in different areas. Some people like certain things more than others, and so that is why all the different opinions on which is best. But compared to where you are right now there is no doubt, they all are better.