The fact that he got Sage Mode wasn't luck.
The Toad Sage probably knew he was going to need it and gave him the power of the Toad.
The fact that he got Sage Mode so fast is impressive as well...
Actually he uses shadow clones to do the vast majority of the work realistically if it wasnt for shadow clones he would still be trying to add the wind element to the resengan, No one talks the forbiiden jutsu that he uses almost all the time and its people like him as to why that jutsu is forbidden. And lets not forget about the gift that he got from 6 tail beasts, or the fact that he was given the nine tails, or has been taught by at 5 sensai's while sasuke has only had 3 (im even counting the teacher they had while still in the academy)sasuke has been out on his own getting better just because he doesn't manga time for his training doesn't mean its not happening.
The shadow clone training method was just a plot device to make him stronger extremely fast. Honestly, it killed the whole "untalented people" thing.
If it hadn't been invented, Naruto would be just as strong as he is now.
This is a manga, and the characters are as strong as the author desires. The main character is always as strong as he needs be.
But you're right about Sasuke training off screen. He probably does.