[The Saucepan Man]

In the letters it states that Gandalf would have been able to control the one Ring, so it is almost a fact that he wouldn't be affected by the "invisibility" of the One ring.

Gandalf may or may not have been affected by the Ring's gift of invisiblity, but he did not consider himself to be immune to its powers. This is clear from The Shadow of the Past, when he is offered the Ring by Frodo:

"No!", cried Gandalf, springing to his feet. "With that power I should have power too great and terrible. And over me the Ring would gain a power still greater and more deadly." His eyes flashed and his face was lit as by a fire within. "Do not tempt me! For I do not wish to become like the Dark Lord himself. yet the way of the Ring to my heart is by pity, pity for weakness and the desire of strength to do good. Do not tempt me! I dare not take it, not even to keep it safe, unused. The wish to weild it would be too great for my strength.

So, if the corrupting power of the Ring would have affected him, why not its power of invisibility? Maybe it wouldn't have affected him in his Maia form, but would it not have had power over him in his incarnate form?