@Darth SadinI'm fine with a Sith who trained himself but he'd be incredibly weak when compared to one with formal training.
There have been plenty of Sith that have visited tombs of deceased Siths and trained beneath them. I'm more than fine with it. Though I will pick which Sith Lord your character awakens, and it won't be his starting off point. He'd have to work for it.
It would also fit as it would give your character a reason to be on Coruscant such as checking the abandoned jedi archives for information on said Sith Lord.