[Boromir88]

Does anyone here seem to subscribe to the idea that IF Sauron did get the ring from Frodo then he could have somehow increased his might to take over Middle-earth under his rule as many seemed to fear?~Sauron the White

I would say so. I think if Sauron got the Ring it would have only hastened his victory. By this time of the Third Age the people of Middle-earth didn't have enough strength left to beat Sauron militarily. As other posters have pointed out in the prior ages. Most of the Elves had left or were leaving by this time, and the dwarves were a dwindling race. The strongest opposition to Sauron was Gondor and they too were down from their 'glory days.' Gondor reached the height of it's power during King Hyarmendacil's reign and had been declining ever since.

The only hope for the people of Middle-earth was the destruction of the Ring. You can find in The Last Debate several times where Aragorn and others say there is no hope to defeat Sauron through strength of arms. Their only hope was for Frodo (or somehow) to destroy the Ring. Had the Ring not been destroyed, Aragorn (and his 7,000 men with him) at the Black Gate would have been defeated. Which leaves Gondor in a tough spot. Sauron had sent an Easterling force to the Dwarves of Erebor and had already beaten them back into Erebor. He had been assaulting Mirkwood and Lorien. Rivendell was a household and a refuge it had no army, so by this time there was no military strength to defeat Sauron. They may be able to hold him off and gain a few victories but in the long run Sauron would have simply overpowered them.

As Elrond and Galadriel both morbidly point out this idea of 'fighting the long defeat.'

‘I have seen three ages in the West of the world, and many defeats, and many fruitless victories’~The Council of Elrond

'Through the ages of the world we have fought the long defeat’~The Mirror of Galadriel

Now you could argue that Sauron actually could be killed again as he was defeated in the 2nd Age by Gil-galad and Elendil. However, I don't think that's likely. Sauron only came out after his army had been defeated, that's when he challenged Elendil and Gil-galad; and in the War of the Ring Sauron showed no interest in leaving Barad-dur...as I think Denethor correctly points out to Pippin:

'He will not come save only to triumph over me when all is won.'~The Siege of Gondor

So, I would say that had the Ring not even been destroyed Sauron would have eventually defeated everyone who opposed him...and had he gotten back the Ring this would have hastened his victory.