Not as you quoted it.
Contrary to what I just said, I've done this successfully with one character here and there and actually in my last two consecutive sessions.
In one, a lone member could appropriately disguise, and successfully went through a long complex, convinced people he was there to see the leader, stealthily unlocked the door and snuck around the leader's room; disguised himself as such (Risky!) and came out the other side (An aside: I also had those players help drawing the map as he went through, which may have helped in the elaborate dungeon)
Why did people care about this? Why was it fine for only one person? They were invested in the result and it was very risky. Cheers around the table on high rolls and concern as he went through each corridor. They were invested because they considered many ideas over that session and felt hopeless at any other approach. This felt like their last chance, so they got him to go through and each roll was a big deal as it could result in the death or capture of their party member.
In a second one, someone they thought they were cooperating with started sprinting off with their evidence and they gave chase. Quickly, three of them were lagged behind severely and the last was jumping creeks, climbing cliffs, and skirting a waterfall as he gave chase; capturing the escapee. (In this case, the other players got to do stuff until they had failed "too badly"; which left a single player performing the chase.)
Again, the players were invested in the actions of the single person being successful. They needed the success and knew it could result in Bad Things happening if they didn't get it. He succeeded and as such saved the party from a harder campaign down the road.
Why were they invested
Because there was a real chance of failure. Why do you watch a show even if you know the outcome? Because you literally don't know how they'll escape; and the ante is upped if you know Death is a real possibility.
So why am I saying no?
Because you aren't saying you want to do it once; you want to do it four times in one session. You will have some very bored players because you cannot keep investment on each one.
One last example where I did as GMNoob suggested:
The PCs could participate in a demi-god's challenge to earn her favor; but had to be worthy combatants. As they entered a portal they were each transported to different arenas where they fought a single opponent in an interesting area.
Side note on the above; which was very risky on my part: If one successfully completes the challenge long before the others would; they will get bored. The Angry GM says that basically any combat where a player isn't making actual decisions for 3 turns should end. So if the only option you have is casting Magic Missile for the 4th time and standing there; the GM dun goofed and should've provided a more interesting scene.
The same goes for the above and why i'm a hard "No." You're looking at having 3 players, for many more than 3 rounds, do nothing at all; and then do that 3 more times.
Fine, how do I fix it?
Have them select a single player to run the gauntlet. All are relying on his success or failure. Maybe let them buff him and whatnot before hand; share gear to give him the best chance; and you as the GM better be well prepared for if he fails. If that means he dies and the campaign goes in a different direction; that's what happens. Why? because you need investment.
Finally, ONLY do the above if its the player's choice. My players chose to do the chase, chose to infiltrate the tunnel system, chose to enter the portal. The campaign did not hinge on them doing it; and they could walk away (with some consequence.)
This is what makes them potentially dying OK: They chose an action and knew it was very dangerous. If they die then it will feel just even though it would be depressing. Player deaths suck a lot more when it feels like the GM pushed them into a situation and they couldn't do anything about it.
You could also have a guantlet where other players can pull levers to affect it; making it more or less challenging depending when they pull various levers. This may have them running around testing them before the first PC gets there, remembering and coordinating the use of levers as the main PC moves through. I think i'll have to loot this idea.
I believe a scene like this exists in the various Saw films.