Yes, but that's also very unlikely as this isn't the working of the Wheel as depicted in the series (nor as Jordan implied it works), and Jordan was the sort of worldbuilder who felt he needed strict rules for pretty much everything (Brandon is the same, he loves the challenge of making up a lot of rules and then force himself to stick to them. He finds his creativity is motivated by this, as he's forced to find ways to make happen what he'd like to happen in the story). So, the Wheel weaves toward certain things, make different threads cross one another to achieve what it needs, over many generations. It introduces macro "rules" rather than micro manage things through "miracles". It can't twist things so Rand becomes simply invulnerable to the True Power etc. It won't create Heroes, it chooses to make heroes out of worthy souls, with characteristics it can used. Or, for example Min isn't unique, the Wheel has rather re introduced the possibility the Talent, and wove things so Min has it. It's the same for Perrin. The Wheel has not magically made him a wolfbrother, it re introduced the Talent into humanity and wove the Pattern so Perrin has whatever it takes to become one.

It did not choose Tam al'Thor and the Two Rivers at random (that he would raise among "the old blood" has been prophecized millenia ago), the whole ancestry of Rand, Mat and Perrin has been many generations in preparation. You might even say that the History of the area has been shaped so the old blood remained true there, in preparation for the last battle and Rand, Perrin, Mat, Egwene, Nynaeve etc.

That's why we can pretty much assume that Rand's genetic baggage has been shaped through many generations, rather than introduced "magically" by the Wheel when Rand was ready to be conceived.

Jordan has explained channellling is a combination of characteristics of the soul and genetics (he even decided what sort of genes were required). It's part of his "rules", so it's pretty safe to assume the channelling abilities of the characters all stick to these rules.

Years ago, someone with some knowledge of genetics has calculated probabilities for the characters we know the ancestry of. IIRC, Galad was an unknown, because of Morgase (who could learn) and Tigraine (who couldn't), which left us in the dark about Taringail's genetics. Some have speculated Jordan made Moiraine the half-sister of Taringail instead of his sister on purpose top stick to his rules, so the Taringail-Morgase union produced channellers who can learn, Janduin-Tigraine produced a powerful sparker, but Taringail-Tigraine produced a non-channeller, because he didn't want Galad to have the ability.

I'll be very surprised if it's revealed Galad can learn, as surprised as I would that Gawyn can't learn (though I'm not convinced this will be used in the series. Maybe... if he's to marry Egwene, she might ask him if he would be tested and agree to learn if he has the ability. There's not much point in going through all the various pains of a channeller/non-channeler marriage, watching him grow old and weak while herself stays in her prime, and for him to watch himself diminish physically and mentally and feel more and more inadequate for her as he grows old, if he can live as long as Egwene. There's not much point for Egwene either to hesitate to have children - as virtually all AS do, fearing the pains of having to watch them die, then her grandchildren, and her grandgrandchildren etc. if marrying Gawyn has 100% chances of producing children with the ability. So I think before the end, if the relationship goes on, when it's widely known saidin is cleansed, and especially in the case that male channellers reunite with their sisters, Gawyn might end up asking to be tested.)

I don't really see the point/interest of making Galad a channeller, however. That's pretty much a non-issue with him. He's a WC, but he doesn't hate or fear channellers. He doesn't want to have no purpose in life, so if he had the ability, he'd insist on learning in order to serve with his skills. Gawyn, it's less certain. I don't think it would be as easy/automatic for him to cope with the fact he has the ability.