[The Squatter of Amon Rûdh]

Given the shortage of information about the fates of the Ithryn Luin, that is certainly a possibility; but I think it unlikely. Firstly, Tolkien does offer his own speculations about the fates of the Blue Wizards in Letter 211 (also cited in Unfinished Tales):

I think they went as emissaries to distant regions, East and South, far out of Númenórean range: missionaries to 'enemy-occupied' lands, as it were. What success they had I do not know; but I fear they failed, as Saruman did, although doubtless in different ways; and I suspect they were the founders or beginners of secret cults and 'magic' traditions that outlasted the fall of Sauron.

Letter #211, to Rhona Beare, 14 October, 1958. Letters p.280. cf. Unfinished Tales, The Istari, endnote 3 (p.518)

Although this is a very vague and uncertain declaration, it seems inconsistent with the idea that Alatar and Pallando were imprisoned in a pair of statues. After all, the Silent Watchers would be unable to start any cults or traditions at all, since they seem unable to communicate except in wails and screams. Personally I think that if Sauron had suborned two of the Istari to his service he would have more important work for them than guarding the tower of Cirith Ungol. They would have been able to cause chaos among the forces of the West had they appeared and begun to contradict Gandalf's messages and advice.

Tolkien says of the Silent Watchers:

They seemed to be carved out of huge blocks of stone, immovable, and yet they were aware: some dreadful spirit of evil vigilance abode in them. They knew an enemy. Visible or invisible none could pass unheeded.

The Lord of the Rings, VI, 1, The Tower of Cirith Ungol, p.902

Sam passes their vigilance twice: once to get into the tower and once to take Frodo out.

[Sam] sprang past them; but even as he did so, thrusting the phial back into his bosom, he was aware, as plainly as if a bar of steel had snapped to behind him, that their vigilance was renewed. And from those evil heads there came a high shrill cry that echoed in the towering walls before him. Far up above, like an answering signal, a harsh bell clanged a single stroke.

Ibid. pp. 902-3.

Sam drew out the elven-glass of Galadriel again. As if to do honour to his hardihood, and to grace with splendour his faithful brown hobbit-hand that had done such deeds, the phial blazed forth suddenly, so that all the shadowy court was lit with a dazzling radiance like lightning; but it remained steady and did not pass.
'Gilthoniel, A Elbereth!' Sam cried. For, why he did not know, his thought sprang back suddenly to the Elves in the Shire, and the song that drove away the Black Rider in the trees.

'Aiya elenion ancalima!' cried Frodo once again behind him.

The will of the Watchers was broken with a suddenness like the snapping of a cord, and Frodo and Sam stumbled forward... There was a crack. The keystone of the arch crashed almost on their heels, and the wall above crumbled, and fell in ruin... A bell clanged; and from the Watchers there went up a high and dreadful wail. Far up above in the darkness it was answered. Out of the black sky there came dropping like a bolt a winged shape, rending the clouds with a ghastly shriek.

Ibid, p.915.

Two things occur to me on reading these passages: firstly, like Shelob, the Watchers can be cowed by the use of Galadriel's phial, and they also seem to be susceptible to the name of Elbereth as are the Ringwraiths. Secondly, Tolkien refers to their will and spirit in the singular, making them into a single entity. This suggests to me that the most likely explanation for them is that Sauron has invested them with some measure of his own malice and power, just as he did with the One Ring. The other, rather less likely, alternative, if these things must be explained, is that the spirit of a Man or Elf has been corrupted and imprisoned in the statues and the gate. I have a feeling that two Maiar acting in concert would just be too powerful for two hobbits to overcome, let alone one on his own.

That being said, though, I think that the Watchers are more effective in their narrative context for their inscrutability. The fact of their malicious will is enough for me: I don't need to know how it got there, and the feeling of the unknown that they evoke adds to their menace. That may even be why Tolkien left them unexplained.