James Potter and co became un-registered Animagi in their school years. Presumably they didn't say anything about it for 2 reasons: first, it would prevent them from spending full moons with Moony; and second, it went against their rebel-without-a-
It seems that being an unregistered Animagus is dangerous (Hermione implied in OotP that Rita Skeeter would go to Azkaban, as her blackmail).
"Otherwise, as you very well know, I will inform the authorities that you are an unregistered Animagus. Of course, the Prophet might give you rather a lot for an insider’s account of life in Azkaban.”
So, why didn't they register as Animagi after graduation, when James went "respectable" under Lily's influence and they no longer needed to hide their spending time with Lupin?
They could simply say they JUST learned to become Animagi; to avoid being accused of being unregistered during their school years.