Guts' story is not for the faint of heart, so read the above background link at your own discretion. But it's safe to say that none of League's Champions have it as bad as him.
Is his FUBAR life too dark for League? Or could we eventually have a story that rivals it?
Gut's story is dark but has good moments (by which I mean light) that pop up every now and then throughout a massive story that is still not finished. I think Muerta (probably got that wrong) said he wasn't even 1/3rd of the way done in the story.
League of legends lore is not that long.
Plus we have Darius.
Almost certainly not.
Can you imagine a champion witnessing his girlfriend being brutally raped in front of him after all his friends were dismembered as a huge part of their background?
Berserk is 2grim4LoL.
To be fair, its gonna be hard to make a backstory as dark as Guts without putting alot of time into developing the story. Atm though, Master Yi's old lore is pretty dark.
Without going into full 40k grimdark, unlikely. Runeterra is too people friendly.
Actually 
seems to be pretty much an expy of guts.
I mean he is a really angry dude with a huge black sword and his archenemy is a somewhat feminine looking male demonic being,who belongs to a group of 5 of these beings,who killed the family/friends of the berserker and who is seen as a hero by some,despite the fact that he only cares about himself.(bonus points for femto being red in the original anime)
So yeah tryndameres story is almost as bad as guts.
