Well, no. Just like Wendy and Natsu, Garjeel's dragon disappears on the same day when he was a little kid. Rogue wouldn't have been looking up to Garjeel before then, and couldn't have become a Dragon Slayer afterwards.
Unless Sting and Rogue somehow found dragons that somehow didn't disappear along with the rest of them, there's no way they could have been taught dragon slaying from real dragons.
Also rememeber that Garjeel and Natsu and Wendy got stopped in time for 7 years. So as young as they are now, Sting and Rogue probably weren't even born yet on the day the dragon's disappeared.
Arcnologia is also, like, the MOST powerful dragon(and not even really a dragon), so I don't think he's a good judge of the power of your average dragon.