By arriving at the scene, <PERSON> certainly made a very clear pathway for extracting the stone from the mirror. We can't know for sure what might have happened had <PERSON> not been there. Perhaps the mirror would have prevented <PERSON> from getting the stone altogether -- <PERSON> seemed to think it was effective protection -- or perhaps not. <PERSON> can be very determined, after all.
To answer the title question, though: yes, <PERSON> and co. did save the day: <PERSON> did not get the stone, and in fact, was set back a few paces, directly as a result of the actions of <PERSON> and friends. But also yes: they very nearly did lose the day. Things could have gone badly if <PERSON> never had a chance to discover the effect his own skin could have on <PERSON>.
As to the final question - "were the adults correct all along that 'our heros' were meddling outside their competence?" - it's worthwhile to point out that perhaps not all adults held this view. <PERSON>, in particular, might have specifically intended <PERSON> to get to the final showdown. 45
As we see <PERSON> ruminating at the end of the book:
"D'you think he meant you to do it?" said <PERSON>. "Sending you your father's <PERSON> and everything?"
"Well," <PERSON> exploded, if he did – I mean to say – that's terrible – you could have been killed."
"No, it isn't," said <PERSON> thoughtfully. "He's a funny man, <PERSON>. I think he sort of wanted to give me a chance. I think he knows more or less everything that goes on here, you know. I reckon he had a pretty good idea we were going to try, and instead of stopping us, he just taught us enough to help. I don't think it was an accident he let me find out how the mirror worked. It's almost like he thought I had the right to face <PERSON> if I could...."
This vaguely resembles <PERSON>'s own words when he later on reveals information to <PERSON> in the Deathly Hallows:
"We have protected him because it has been essential to teach him, to raise him, to let him try his strength," said <PERSON>, his eyes still tight shut. 417