I just heard it earlier today (same video you sent me, too. Weird. XD) and I absolutely love it! <3 This song = FTW. =3 It reminds me of the awesome ones from Johto.
No, I haven't heard the full version. TT~TT I hadn't realized they had one. But I did hear the full version (hell, I think it's even my YouTube video on my profile) of Docchi~Nyo.
But then it's not April Fool's. XD It'd just be a prank. Personally, I prefer to prank whenever I want. And it's usually not on April Fool's day or anywhere near it.