It totally seems like something they would do, but I don’t think so.
Amazon had a pilot for Dark Minions:
Gone now, but it was going to be a series from the perspective of two expendable minions.
Oh–Frylock are you thinking of the Venturestein episode? That episode does kind of do that now that I think of it.
On the American masterpiece, Phineas and Ferb (Disney), the evil Dr. Heinz Doofenshmirtz regularly shared backstories about why he was evil…
here are a few montages…
In the Ultimates 2 , Marvel’s take on the Avengers in the Ultimate Universe (everything is more gritty, dark and just a tad more realistic) the main group of villains are The Liberators.
One of them, the Colonel, is first seen in an earlier issue when Captain America ‘saves his country’ and he’s not thrilled by it. This event turned him onto a path of hatred towards Cap and the USA.
Although not a henchman, especially since We Were Soldiers attempts to show that the Vietnamese were – well, not good, but not more evil than the American soldiers, the Vietnamese soldier who is standing behind a large tree summoning up the courage to charge the Americans counts. If I recall correctly, he is thinking about his former life as a student and his significant other (and probably, between the lines, how he got subsequently drafted and would rather not be here but is also somewhat doing his patriotic duty).
Then he finally charges the American lines through the bush, and the scene abruptly cuts to the Americans who are in the midst of close quarters combat when a Vietnamese soldier jumps out of the bush, only to be immediately shot by an American with a pistol, and then the fighting moves on like it was no big deal.
I remember seeing a video on the Internet years ago which was the back story to the sword-weilding henchman that Indiana Jones shoots in the first film (the bit where it looks like a big fight is going to happen and Indy just shoots him). He was fresh out of jail and had been to visit his relatives then had to do one simple job etc. Have never managed to find the video again though 
The title characters of Rosencrantz and Guildenstern Are Dead couldn’t understand why they had to die to become a line in a play.
In Joker, the story is told from the POV of Joker’s henchman, Jonny Frost. Frost becomes enmeshed in the wild roller coaster ride of Joker’s chaos and schemes, and meets his own demise at the end.