I'm not sure how much you know about child psychology or childhood development. But the more you learn about this area the more you realize that the things children are exposed to at a very young age have an outsized impact on their development as they age.
There is a growing body of research that tells us what children are exposed to (or experiences they've had, like whether someone read books to them at ages 2-5 or not) has a strong correlation to some surprisingly outcomes later in life.
So if they can show it, or make it part of an education curriculum. Or mess with the algorithms to make sure it's being popped up as recommended content for children, by children, for children, over say that old Roadrunner cartoon. It would have some degree of impact.
Also, if Clan Wolf is engaged in this kind of thing, it isn't probably ONLY this one cartoon. It's probably a multi-pronged approach across different age groups and in different formats. One cartoon by itself may not do a lot. But three cartoons over here, a few books over there, a few ads, efforts to put some Terrans and Clansmen side-by-side at work or in a community so they start to see each other as just people and not just stompy 'mechs. A comprehensive approach would likely have an impact yes.
Versions of this have been depicted across so many scifi and historical shows. The adults don't like the invaders and perhaps are part of a resistance movement even. But the child or children are going to school every day and being exposed to the invaders' version of events, plan for the future, and depiction of themselves (aka propaganda). So as the adults continue to view the invaders as the invaders, the child or children are being subverted into thinking the invaders are actually friends, they aren't that bad, they are good even. Sometimes it goes so far that the child even turns in the adults as traitors as part of the story.
This is an incredibly common portrayal of this kind of thing. Enough so that I think most BT players wouldn't bat an eye at seeing it happen here. Especially if the writers explained it well.