No, it doesn't seem to be a traditional Irish saying.
Quote Investigator, a site which is extremely good at ascertaining the origin of quotes, has a page about a similar saying and its evolution and origins:
Never attempt to teach a pig to sing; it wastes your time and annoys the pig.
-- Robert Heinlein, Time Enough for Love (1973)
There’s no profit in teaching a pig to play the flute. Even if the pupil could learn, others would do the business better. There are persons who have no capacity for learning a certain art, and teaching it to them would be lost labour.
-- Charles Haddon Spurgeon, The Salt-Cellars: Being a Collection of Proverbs Together with Homely Notes Theron (1889)
The same saying and variants have been discussed on English Language & Usage Stack Exchange, without any reference to Celtic tradition.
In the Wheel of Time series, you will find a great many "old sayings" attributed to various characters or traditions within the story (especially when a character called Lini, and other characters who were raised by her as children, make their appearances later in the series). There are so many, and some of them specifically referring to fictional cultures or peoples within the Wheel of Time world, that it's safe to assume most of them were invented by Jordan himself.
Definitely not all of them, though, so this is still a reasonable question. Jordan was clearly well versed in many different cultures from around the real world, elements of which can be seen in the various fictional cultures which he spent the 14-book saga developing. Notably, the Shienaran saying "Death is lighter than a feather, duty heavier than a mountain", which fits the Borderlander culture so well that many people assume Jordan invented it, was actually part of the Imperial Rescript to Soldiers and Sailors from pre-WW2 Japan.
You say that "The Wheel of Time saga [...] appears to have a strong Irish influence", but on a broad scale, it's rather influenced by many different cultures from all over the real world. What you've seen so far, in the first half of book 1, is perhaps more influenced by Celtic culture than others, but that's because the Two Rivers, like the starting points of so many other high fantasy series since Tolkien, is inspired by a vision of the ancient rural British Isles. In fact, Jordan deliberately started his story in a way reminiscent of Tolkien, to make fantasy readers feel like they were in a familiar setting, but after the early parts of book 1, The Wheel of Time swiftly goes in very different directions from The Lord of the Rings.
