Implausibility isn't the problem--given that Cody exists, we know that Casey and April will have at least one child, so why not Shadow? The problem is that the circunstances which brought about a teenaged Shadow in the comic books--an attempt to work something resembling a real-time chronology in a series with a then-sixteen-year-old history--are vastly different from the show's, which is "only" five years old, tries not to acknowledge the passage of time at all, and attempts to keep the protagonists as Teenage Mutant Ninja Turtles. Master Moron's suggestion is the simplest and most likely to work (and gets kudos from me for including Gabrielle), but would eliminate what I believe is a key element of the character, the fact that she was partly raised by the Turtles and Splinter, and thus grew up into the weirdness--you might as well use an established character like Angel if you want to introduce a teen Shadow to the turtles. CyberCubed's suggestion would be a decent, elegant compromise, and I would love to see small time gaps like that (I like the idea of long chunks of time where nothing exciting happens) but I really don't see it happening as a regular thing--not only would it mean constant redesigns for some characters (althought this may not be a problem for people who redesigned Baxter Stockman fourteen times), and the producers may think the audience would find such gaps hard to follow. Then again, if Legion of Super-Heroes could incorporate a time gap between seasons, perhaps its not impossible here.
Hell, it occurs to me that a combination of both ideas could work: Gabrielle leaves a four-year old Shadow with Casey, and we eventually see her grow through a series of small time gaps.
Yeah, I was thinking mostly of American cartoons, and Goku's family never actually crossed my mind. In any case, do we ever actually see the period around Gohan's birth? Don't they go from a childless Goku and ChiChi to suddenly having an infant Gohan? In any case, feel free to correct me, but I don't think such a thing is common in anime either.