[Fingolfin II]

In addition to what Boromir has said, if Gimli made it to Sammath Naur, even he wouldn't be able to give up the Ring and if he already killed Gollum (as Nil said) then there goes the Quest. Without Gollum, Middle-Earth would have been doomed, as no-one (in Middle-Earth)- except Bombadil, as Boromir said could give up the Ring in the heart of Sauron's domain-

'Yes' said Frodo. 'But do you remember Gandalf's words: Even Gollum may have something yet to do? But for him, Sam, I could not have destroyed the Ring. The Quest would have been in vain, even at the bitter end. So let us forgive him! For the Quest is achieved, and now all is over. I am glad you are here with me. Here at the end of all things, Sam.'

So here we see how important the connection formed between Frodo and Gollum really is- if Gimli was in Frodo's position, he would not have the ability or empathy to connect with Gollum (despite being a Ringbearer), which I think could only be found in a hobbit, thus he would have probably not have given Gollum any chances and the Ring would have been captured. Or the reverse- Gollum may have slain Gimli in anger and revenge; look at his attitude towards Frodo's kindness and his attitude towards Sam's suspicion. Gimli, I believe, would have been inclined to treat Gollum like Sam, and thus no bond of understanding between Ringbearers would have been forged.

There is no question that Gimli would have succumbed to the temptation of the Ring in Sammath Naur. Let me give two quotes to help explain why-

At first he could see nothing. In his great need he drew out once more the phial of Galadriel, but it was pale and cold in his trembling hand and threw no light into that stifling dark. He was come to the realm of Sauron and the forges of his ancient might, greatest in Middle-Earth; all other powers were here subdued.

The 'darkness' of Sauron's ancient forge must be pretty powerful, if something that shines with the light of a Silmaril cannot light up his forge. Equally, I believe that the 'all other powers were here subdued' quote applies to the mental will of those in Orodruin and their capacity to overcome Sauron's will.

But that he [Sauron] never contemplated or feared. The Ring was unbreakable by any smithcraft less than his own. It was undissolubl in any fire, save the undying subterranean fire where it was made- and that was unapproachable, in Mordor. Also, so great was the Ring's power of lust, that anyone who used it became mastered by it; it was beyond the strength of any will (even his own) to injure it, cast it away or neglect it.
-The Letters of J.R.R. Tokien (No. 131)

I think that this dispells any doubt about whether Gimli would have become corrupted by the Ring or not- if Sauron himself couldn't destroy it, then I'm pretty sure Gimli wouldn't be able to also. In answer to your original question, Zebedee, the One Ring was much more powerful than the 7 Dwarf Rings and had a greater potential to corrupt- so yes, sooner or later, the Ring would inevitably corrupt Gimli; even if it took so long that it corrupted him in Sammath Naur, the heart of Sauron's realm.