I regret that I do not have access to the article by Johnston, but I understand his gist from Susan’s answer.
First of all, the argument that “research has failed to turn up any evidence for the use of eunuchs as officials in Egypt” is likely to convince only those who believe that the story of Joseph is an authentic record of historic events. It will not have much weight with those who believe that the whole account of Israel’s captivity in Egypt and subsequent salvation by Moses is part of a national mythology, possibly a back-projection of the historic captivity in Babylon. But we need not linger with that.
To stick to the hard linguistic data: It is widely held, and probably correct, that Hebrew sārīs, Aramaic srīsā is a borrowing from the Akkadian ša rēši, literally “of the head”. This occurs frequently in Akkadian texts of all periods as the title of some court official, but it also occurs in at least two texts unambiguously in the meaning “eunuch”. (See the CAD, volume “R” pp. 292-296, especially at the very end of the entry). More precisely: the Hebrew and Aramaic words would seem to derive from Middle or New Assyrian, with the typical later Assyrian shift of /š/ to /s/. Johnston is thus not right to say that the Akkadian usage did not “any connotation of sexual impotence”.
But this is where I have difficulty with the “pre-exilic: court official, post-exilic: eunuch” part of the argument. Since the Akkadian ša rēši means both “court official” and “eunuch” the “diachronic shift in usage” would seem to imply that Hebrew borrowed the Assyrian word twice, first in the meaning “official”, and then again later in the meaning “eunuch”. That is not impossible, but it is not a very attractive proposal. Or else you could assume that Hebrew sārīs all along had both meanings and that it is mere coincidence that the second meaning does not show up unambiguously until the post-exilic period. But in that case the conclusion that in pre-exilic texts sārīs must mean “official” is not tenable.
I add that in the Aramaic languages srīsā clearly means “eunuch”, not “court official”.
This does not imply that it must have this meaning in the Potiphar story, but it does mean that you cannot rule out this interpretation.
By the way, high ranking married eunuchs are known from mediaeval Arabic texts. See Encyclopaedia of Islam (2nd ed.), article “khāṣī”, esp. p. 1090 col ii (excellent article by Charles Pellat). The Talmud (Yev. 8,4) also mentions the “wife” of a eunuch in the context of a Levirate marriage.