No, SkyDrive was always centralized server-side without any of the conflict resolution coauth concepts that Groove had. It was a completely separate project.
What about OneDrive For Business? I recall the executable was, confusingly, Groove.exe for quite a long time.
As I recall, OneDrive for Business had absolutely nothing in common with OneDrive except that marketing in all their wisdom decided to throw that name on it for maximum confusion (a very popular technique at Microsoft - see also Skype for Business). I don't know its history, but assuming it evolved out of some Sharepoint product it wouldn't surprise me if it had some Groove DNA.