Lincoln's 10% Loyalty Oath plan was meant, not only to just get the states back in ASAP, but also to show a bit of forgiveness and understanding to those who seceded because of him. Sort of gaining their faith in the fact that he is NOT a tyrant and dictator like they thought. His assassination changed all that.
The Wade-Davis Bill (the 50% IRONCLAD Loyalty Oath) was the Congressional attempt to punish the south, AND rub their noses in it. The Ironclad oath meant only those who had ALWAYS been loyal to the Union could take it. Well, that eliminates 90% of the southern whites, men and women (and at the time the women were treated little better than children and didn't have the right to vote, so they were summarily ignored anyway). That left the Freedmen, the Carpetbaggers (northerners looking for a quick buck, some cheap land, or a pretty lady), and Scallywags (southerners who never supported the CSA, or feigned it until they could collaborate with the Yanks).
Johnson's Amnesty Plan was a mix of the two, with a 50% loyalty oath, but not ironclad. That was pretty much all he did, because Congress by this time was almost soley Republican, and they decided that the southern congressmen weren't lawful, and were thus barred from Sitting. This way, the Republican dominated congress simply overrode Johnson's Vetoes (of which there were many) and that's how we got the Military Reconstruction Act, the Commander of the Army Act, and the Civil Rights Act of 1875, and so forth. Johnson had zip to do with them. Hell, the Commander of the Army Act was passed so that Johnson couldn't be Commander in Chief (effectively).
The one thing that really hamstrung any future southern rebellion was the fact that they had to repudiate their state debts. In essense, any amount of Reb money that was used to service the CSA in ANY WAY, including all the bonds, and I.O.U.s, was taken and trashed. So John T. Reb the friendly farmer who just thought he'd buy up $100 bond for a $112 return in a couple years lost not only his savings of $100 but was one of those guys who couldn't take the Ironclad oath. This is the main reason (seconded by the damaged done in the war) that the southern states went from the Wealthiest States in the Union to the Poorest States in the Union (even today!). Alabama (who sent the most people per capita to the war in 1861--and still sends a disproportionate ratio today) is 49th in the nation of wealth. Mississippi is 50th. I'm an Alabamian, and I have some Southern Pride... I'm not sure where it came from, but there it is.
My point with that history lesson is this:
Had Congress been less stringent after the war, the South would have been less hostile in the aftermath; the Black Codes and all the rest of the mess. If Lincoln had not been assassinated, his plan was much more forgiving, but still with a strong military presense. If Lincoln had survived, the south wouldn't have been both broken militarily AND economically, but would have had a chance to overcome the industrializing profiteers and the Boll Weevil repercussions later in the century.
So to answer your question, the South was not as loyal as it could have been, mostly due to the rabid nature in which Congress treated the post-war legislatures of the South (understandably, as many of the CSA officials had been reelected).
