It's possible, in a very indirect sense, that they're related, but the timing is suspect, and it's more likely he caused the salvation of his son and the other surviving Númenóreans (i.e., the Dúnedain).
As you mentioned, Amandil set sail to try and get a pardon for the sins of the Númenóreans, but nothing is known about his success or failure. That takes place towards the end of the Second Age. After his excursion, several things happen:
- The downfall of Númenor
- The miraculous survival of a number of Númenórean ships
- The establishment of Arnor and Gondor
- The War of the Last Alliance, where Sauron is defeated by Isildur
- The end of the Second Age and the beginning of the Third Age
- The corruption of Isildur
- The collapse of the kingdom of Arnor
- The corruption of Mirkwood
It's only at this point do the Istari enter the picture, as mentioned in Of the Rings of Power and the Third Age:
Even as the first shadows were felt in Mirkwood there appeared in the west of Middle-earth the Istari, whom Men called the Wizards. None knew at that time whence they were, save Círdan of the Havens, and only to Elrond and to Galadriel did he reveal that they came over the Sea. But afterwards it was said among the Elves that they were messengers sent by the Lords of the West to contest the power of Sauron, if he should arise again, and to move Elves and Men and all living things of good will to valiant deeds.
The Unfinished Tales story, "The Istari", establishes the arrival to be about 1000 TA. There, the motivations for sending the Istari are broad and vague, but no mention of a singular, direct cause is made:
Emissaries they were from the Lords of the West, the Valar, who still took counsel for the governance of Middle-earth, and when the shadow of Sauron began first to stir again took this means of resisting him. For with the consent of Eru they sent members of their own high order, but clad in bodies as of Men, real and not feigned, but subject to the fears and pains and weariness of earth, able to hunger and thirst and be slain; though because of their noble spirits they did not die, and aged only by the cares and labours of many long years. And this the Valar did, desiring to amend the errors of old, especially that they had attempted to guard and seclude the Eldar by their own might and glory fully revealed; whereas now their emissaries were forbidden to reveal themselves in forms of majesty, or to seek to rule the wills of Men or Elves by open display of power, but coming in shapes weak and humble were bidden to advise and persuade Men and Elves to good, and to seek to unite in love and understanding all those whom Sauron, should he come again, would endeavor to dominate and corrupt.
So given all the shenanigans Sauron pulled between the disappearance of Amandil and the arrival of the Istari, the connection seems at best tenuous. The Valar were not that slow to act: they sunk Númenor like a battleship pretty quickly after the plot was revealed. So it's more likely the more proximate intervention, the salvation of the Númenóreans who sailed east, is what Amandil managed to accomplish assuming he ever made it to Valinor.
