How do you complete Got the Basics hidden quest in Hearthstone? Would leveling all heroes to level 10 do?
Got the Basics! : Collect every card in the Basic Set.
You're exactly right.
There are two distinct groups of basic cards -- the neutral basic cards (of which you start play with all of them unlocked), and the class-specific basic crads (of which half start locked, and the other half is XP-locked).
The last basic cards for each class unlock at level 10, so if you level all 9 classes up to at least level 10, you will have acquired all of the basic cards, and trigger the hidden quest.