No chance, he can't take advantage of plot devices like Superman could. And he's not a great majestic character so his story isn't strong enough to resist Mandrakk. Either way Darkseid just OS him.
__________________
“Where the longleaf pines are whispering
to him who loved them so.
Where the faint murmurs now dwindling
echo o’er tide and shore."
-A Grave Epitaph in Santa Rosa County, Florida; I wish I could remember the man's name.
Unlike with Superman, Darkseid has no reason to let Thanos live. Just like Thanos has no way of being transported into the Cosmic Armour, let alone controlling it.
Does he get help from the Monitors or access to the Miracle Machine? If so, he stops both Mandrakk and Darkseid. He uses this prep time to travel back to Marvel and brings in Adam Warlock (post Conquest/pre-WOK) and a cosmic cube. Warlock puts on the Cosmic Armor and destroys Mandrakk. Thanos uses the MM to wish for a happy ending. Warlock, after learning the vibration song, sings Darkseid out of existence. Mandrakk comes back only to run into Thanos and Warlock who uses the Cube to form a stake and stab him to death and thus filling Thanos' earlier wish of a happy ending.
And please, Warlock's story is easily equal to that of Superman's. In fact, Superman's story is unique to DC but only because it's contained within DC. If you count other fictions, others are equally as good if not better and Warlock's is one of them.
Where was this stated in FC? The Monitors pointed out that the story of a child from a dying planet was sent to Earth and become it's greatest protector. This story of Superman is why his story was greater than Mandrakk's.
LOL. Found something interesting while looking up to see if Superman was the first super hero. Apparently, the Phantom and the Shadow came before Superman. But then I ran into this guy: Mandrake the Magician.
My point is your scenario wouldn't work. Adam Warlock wouldn't be able to use the Cosmic Armor.
Plus I don't think Thanos is allowed to go back to the Marvel Universe.
Why not? Warlock's story is outside of DC universe. His story is just as compelling as Superman's. Without going back to Marvel or access to other fictions, the answer is pretty obvious. Thanos' story isn't unique; you might as well ask if Darkseid, Wonder Woman, Batman, Peter Parker, or Captain America they can beat Mandrakk. They can't because they can't put on that armor. But given that Thanos is an intellect and has prep, this is how he would achieve this goal.