playing on Leaf Green and went through 5 ultra balls trying to catch snorlax with 1 HP, cought it on Fire Red at 10% health still with one. Difference was my Pokemon was asleep on Leaf Green, and I cought it straight after using awaken on MY Pokemon. Was this just bad/good luck?
No, status ailments on your Pokemon will not alter your chances of catching a wild Pokemon. What happened to you was simply coincedence.