Could Aragorn have won the Battle of the Black Gate without Frodo?

Question

With reference to material from the books as quoted in this question, it appears Aragorn's army gained the upper hand. Although Sauron sent the Nazgul to turn the tide, the Eagles arrived in time to keep the air battle in check. The battle ended prematurely because of the destruction of the One Ring.

Considering the current state of the battle at that point, is it possible for Aragorn's army to emerge victorious against Sauron's army if the battle is allowed to run its course (ie. if the Ring was neither destroyed at Mt Doom nor recovered by Sauron before the battle's end)?

Edit: I feel like people aren't seeing what I'm looking at. I'm referring to this passage quoted in an answer for the question I linked earlier:

Against the Host of the West was arrayed all of Sauron's hordes of orcs, Trolls, and barbarian Mannish allies such as the Easterlings and Southrons (Haradrim). An exact count is not given of the number of Sauron's forces, but it is said that they were "ten times and more than ten times" greater than the Host of the West, making it a force of at least 60,000. Sauron's forces surrounded the Armies of the West on three sides, with the Easterlings on the left flank, the Orcs held the center, and the Haradrim on the right. The Armies of the West always had cohesive stability within their center and kept the Enemy from breaking through by force of numbers. The solid infantry squares of Gondor infantry beat off their inferior Orcish opponents while the Rohirrim cavalrymen staved off the archers of the Harad. The small force of Easterlings launched a quick attack before being repulsed by the armies of Gondor and Rohirrim while the larger Haradrim force slowly retreated to the hills. By now, pressure had eased off of the flanks of the Armies of the West, who smashed into the lines of the Orc-host, slowly beating them off and forcing a retreat back through the Black Gate (though not without suffering sizable losses of their own).

If the army of Mordor, after emptying the land of his dark host, still ends up in retreat before Aragorn's advance, does it not mean that the odds of victory is actually more than negligible if the battle is permitted to play out with the Ring neither destroyed nor returned? The Army of the West is no longer outflanked, the Orcs couldn't hold the line, the Nazgul were focused on the Eagles.

Answer 1

I hesitate to say "no", but it seems incredibly unlikely. From Return of the King (emphasis mine):

The Captains mounted again and rode back, and from the host of Mordor there went up a jeering yell. Dust rose smothering the air, as from nearby there marched up an army of Easterlings that had waited for the signal in the shadows of Ered Lithui beyond the further Tower. Down from the hills on either side of the Morannon poured Orcs innumerable. The men of the West were trapped, and soon. All about the grey mounds where they stood, forces ten times and more than ten times their match would ring them in a sea of enemies. Sauron had taken the proffered bait in jaws of steel.

^{Return of the King Book V Chapter 10: "The Black Gate Opens"}

And (emphasis mine):

All about the hills the hosts of Mordor raged. The Captains of the West were foundering in a gathering sea. The sun gleamed red, and under the wings of the Nazgûl the shadows of death fell dark upon the earth.

^{Return of the King Book VI Chapter 4: "The Field of Cormallen"}

The probability of any army defeating a force more than ten times its size is, while not quite zero, exceedingly low.

Answer 2

It's been years since my most recent reading of the books. Unfortunately, I don't have access to them now, so can't provide quotes. However, my recollection is that nearly all the leaders on Aragorn's side - including Gandalf - considered it a hopeless cause in terms of expecting to win the battle on the battlefield. They were vastly outnumbered, many of their troops were not well trained, and they were weary, having already fought a big battle. So, to answer your question: No, Aragorn's forces were not going to win ... or if you want to go Nate Silver, they had a very, very small chance of winning.

The point of challenging Sauron's forces at the Black Gate was to make Sauron believe they had the One Ring, since if Aragorn (or Gandalf or another strong being) had the Ring and wielded it, they would have a chance to win the battle in spite of the numbers; however, Sauron's actions show that he would still challenge them, hoping to use his superior numbers to re-capture the Ring. Thus, the attack on the Black Gate was a feint by Gandalf and Aragorn to keep Sauron's attention - and forces - outside Mordor long enough to allow Frodo and Sam (with unintentional help from Gollum) to complete the task of destroying the ring.

Answer 3

It certainly was never the plan to win this battle by military means. At Tʜᴇ Lᴀꜱᴛ Dᴇʙᴀᴛᴇ,

[said Gandalf]...‘This, then, is my counsel. We have not the Ring. In wisdom or great folly it has been sent away to be destroyed, lest it destroy us. Without it we cannot by force defeat his force. But we must at all costs keep his Eye from his true peril. We cannot achieve victory by arms, but by arms we can give the Ring-bearer his only chance, frail tough it be.
‘As Aragorn has begun, so we must go on. We must push Sauron to his last throw. We must call out his hidden strength, so he shall empty his land. We must march out to meet him at once. We must make ourselves the bait, though his jaws should close on us.

and

’I do not counsel you to leave the City all unmanned. Indeed the force that we lead east need not be great enough for an assault in earnest upor Mordor, so long as it be great enough to challenge battle.

So, the alliance was fully aware that they would scarcely be able to win the Battle of the Black Gate, but had to fight it nevertheless in hopes of helping Frodo this way to destroy the Ring.

Answer 4

I think all answers will be opinion based - but in terms of precedent, one could assume that like the Battle of Dagorlad - Sauron have would entered the fray himself (in his less than coporeal, weakened state but still attempted to intervene none the less, if, as the purpose of the ruse was, to make Sauron think Aragorn had the ring)