With how important objectives are, would it be possible for a team to successfully pull off a 1-1-1 with 2 junglers?
Hear me out - constantly invading enemy jungle, synchronized ganks on mid lane, and putting enough pressure on bot to ensure they can't constantly be attacking bot lane under tower.
Double jungle?
What does it mean?
to have a good double jungle you still need to fill a basic minimum of capacities as a team
effectively you need an amount of tank busting, damage shred, and supportive capacity in your new role layout. you would have to have a very roam intensive mid laner probably making your mid lane options champions like 
Your bot lane would likely be going against a 'traditional' support+carry duo. so you would need to plan around this accordingly. I would assume that jungler B would effectively be a supportive champion who would get their carry off the ground, the bot lane player would have to be someone who could 1v2 at a fairly early point effectively being a gatekeeper
many top lane fighters and mid lane mages can do this. After about an item a champion like 
can probably 1v2 against a traditional bot lane duo
so jungle b would have to also consider their starting item, would they start a support item? or would they start a jungle item and demand a leash.
Top lane would likely be champions who can handle the mobility issues, I'd assume it would be very split push heavy.
as for the junglers? I would imagine tanks for their sheer utility based on these comps, though hyper mobile duelists might also come into the fold
it would be a constant gank fest eventually graduating into constant team fights. which is why map presence, team fight control, and split push viability would all be really important.
I'd expect a lot of 
and with the viability of champions like expanding i'd actually predict a constant 4v5 with the other side of the map being the guy who lost top lane trying to shove in a t2
EVERYTHING can (CAN) work, including playing with no junglers at all. So yeah: is possible, but i'd say mostly cause is something unexpected. In other words: almost certainly not something that can be truly viable in the long run (or some pro team would have did it already).
Ive dealt with it b4 as a jungler and it is AIDS
Basically the strat is clear and counterjungle and basically make the enemy team minus a jg.
Why split the bad jungle exp?
This sounds like a flex que strat. As someone who mains ADC I would never be up for it.
If you're duo'd or in flex... yes, it can work. You need coordination.
Me and my friends have done this exactly 11 times with a shyvana and karthas bot lane when we are on red side. as shyvana i leave lane and counter jg whenever I get the freedom to do so. karthus doesn't deplete mana that fast allowing you to stay in the 1v2 lane longer. just farm up under tower and if they do decide to turret dive you then you will more than likely kill them both with your passive. You will also want karthus to take tp. all the while shyvana is steeling another red buff and gaining vision control of the bottom half of the jg. this works especially well against a kindred because not only are they loosing out on jg exp they also cant stack because there is nothing left to stack with. We had a 10 game win streak with this strategy and lost our 11th, and have since retired it, but this post is making me want to try it again.
There was a diamond "smite support Singed" one-trick who got banned for this. Riot had to change their rules and unban him after huge public outcry.
So.... Yes. But it's risky.
I have enjoyed a mao/teemo jungle, xerath bot, jhin either mid or top, and then any cleaner to quickly jump in and sweep up leftovers. Even if you do bad, team fights win with traps, mao saps are % max hp magic dmg and what isn’t killed in one hit is cleaned up by other traps or your high range team. Mao can focus build hp later and start baiting heavily and tanking. Champs with pulls and any with high jungle mobility are also very nice.
I suppose if you picked a champion for ADC/APC who can forcefully shove the wave out everytime they attempted to get it under tower it wouldn't be unmanageable but it's hard to synergise with your team with two jungles as it's not traditional - I think the optimal state of the game is how it is lane wise now but it's not an absurd idea, certainly can be put into practice
The short answer is no.
The long answer is it can work especially if you have coordination with a team, however, the top section of the map still doesn't have much for objectives and taking another player off bot lane (the only available lane with two people in it) weakens control on dragon and the bot lane tower which is easier to push down early.
Exactly as you say objectives are very important with the dragon being the most important. You would not purposefully weaken dragon control in order to have a second jungler who could invade the enemy side. Being able to take the enemy second buff < having dragon buffs.
Besides, the jungler is already under leveled, so then you would have two under leveled players on the same team. Also, being able to invade implies lane priority, which you are automatically giving up somewhere in order to have the second jungler and some enemy junglers are not good invade targets. If you can't invade then you have two junglers starved off only one side of the map. Not to mention when your own team is ALSO trying to take your buffs, like giving your ADC the red or your mid laner the blue.
If only you were on EUW... I heard Twitch + Evelynn combo nicely when counter-jungling.
Objectives are very important, and so is assisting.
With how often teamfights break out before the 14 min mark, double junglers means people will be much more prepared for the outcome.
However that essentially means a lack in cs in the jungle, making two people have "Support budget" and three with normal budget in gold.
This also means people constantly monitoring lanes and duo quick objective capturing without out-of-jungle help.
But it also means more threats in jungle with combos, as a Rengar / Ivern double jungle won't give you the chance to early game.
It would be really tough on your solo botlane, since they're going 1v2. You'd need a tank or bruiser to take that lane so they can survive, and if you don't have an ADC, you'll have trouble in the late game. Either the ADC would need to go mid, or be one of the junglers.
