Inspired by here: Why was the ring necessary for Sauron to control Middle-earth?, but not a question about the Ring itself, but about Sauron's military power.
TL/DR: Could Sauron conquer Middle-earth by force without the Ring, and if so why does he still need it to "break the last defences, and cover all the lands in a second darkness", and what use would hiding it be?
To clarify: I'm not looking for answers to why Sauron would want the Ring (eg. to stop it being used against him, or to dominate the Three Rings), but whether a Ringless Sauron was resistible at all, without using the ring being used on either side.
In the Second Age Sauron made the One Ring to give him an edge over the Elves, who were strong enough to resist him otherwise. He succeeded partly, in at least forcing the holders of the Three Rings to stop using them.
By the time of the events of LOTR, however, Sauron appeared to have total "conventional" dominance. He still needed to get the Ring to stop anyone using it against him, but could achieve his goals without it.
To quote Gandalf:
‘Hardly has our strength sufficed to beat off the first great assault. The next will be greater. This war then is without final hope, as Denethor perceived. Victory cannot be achieved by arms, whether you sit here to endure siege after siege, or march out to be overwhelmed beyond the River.
Book V (The Last Debate)
The picture painted here is one where Sauron would be basically as well-off if the Ring was at the bottom of the Sea, or anywhere else where no-one could use it against him. He would win anyway with his armies and retained powers.
However this doesn't fit well with a lot of the dialogue in the beginning of the story, which gives the impression that Sauron could be resisted, as long as the Ring was kept from him:
...The Enemy is fast becoming very strong. His plans are far from ripe, I think, but they are ripening. We shall be hard put to it. We should be very hard put to it, even if it were not for this dreadful chance.
The Enemy still lacks one thing to give him strength and knowledge to beat down all resistance, break the last defences, and cover all the lands in a second darkness. He lacks the One Ring.
Book I (The Shadow of the Past)
The above implies that Sauron needs the Ring to 'beat down all resistance' etc., and that the 'dreadful chance' makes things worse. If Sauron is so strong, he can crush all resistance and defenses without the Ring.
Furthermore, the Council of Elrond has suggestions to send the Ring over the Sea, or to hide it somewhere.
...What power still remains lies with us, here in Imladris, or with Cirdan at the Havens, or in Lórien. But have they the strength, have we here the strength to withstand the Enemy, the coming of Sauron at the last, when all else is overthrown?'
I have not the strength,' said Elrond; `neither have they.'
Then if the Ring cannot be kept from him for ever by strength' said Glorfindel, two things only remain for us to attempt: to send it over the Sea, or to destroy it.'
And a few lines later:
Then, said Glorfindel, 'let us cast it into the deeps, and so make the lies of Saruman come true. ...in the Sea it would be safe.
'Not safe for ever,' said Gandalf. `There are many things in the deep waters; and seas and lands may change. And it is not our part here to take thought only for a season, or for a few lives of Men, or for a passing age of the world. We should seek a final end of this menace, even if we do not hope to make one.'
Book II (The Council of Elrond)
The above, with Gandalf's response, indicates that there would be safety in hiding the Ring from Sauron without using or destroying it, with the danger only returning for later generations. Once again, throwing the Ring into the Sea ought to result in everyone being conquered by Sauron's armies, if he indeed had the power to do so. [Confusingly, the passage also implies at the same time that Sauron could "overthrow all else" and take Rivendell without the Ring]
The above quotes imply that keeping the Ring out of Sauron's hands would allow some hope of survival, which doesn't fit well with Gandalf's statements in the Return of the King about Sauron's armies being unbeatable anyway.
TL/DR: Could Sauron conquer Middle-earth by force without the Ring, and if so why does he still need it to "break the last defences, and cover all the lands in a second darkness", and what use would hiding it be?