For OP's question:
Is the chi (χ) used to indicate the kind of a vowel in the original Hebrew (namley the aleph א), a transliteration as it is from Hebrew in already Hebraic Greek?
The short answer is "No" -- (1) in the first instance, because chi is representing (possibly, more in a moment) a consonantal sound, not a "vowel". Aleph and Ayin are consonants, and although in English transliteration we associate them with vowels, it should not be forgotten that they are in fact consonants. And (2) in the second instance, because whatever the graphic similarity might be (it is pretty slim in manuscripts), this isn't a graphic issue. (See further note below.)
But there is a longer answer. To begin with, the representation of a particular name across languages can often be peculiar. One of my "favourites" to illustrate this is:
Jacob → James → Diego
...all the "same" name, and the relationship between them explicable, but appearing very different! A closer biblical example would be:
- Habakkuk = Heb. חֲבַקּוּק
- Ambakoum = LXX Ἀμβακοὺμ
So ... sort of explicable (the initial vowel, the introduction of the mu before beta; I'm not so sure about the final "m", though).
There are plenty of treatments of how Septuagint (or Koine) Greek handles proper names. One of the more full ones is found in Henry St. John Thackeray, A Grammar of Old Testament Greek according to the Septuagint (Cambridge, 1909), pp. 160-171. He might treat OP's case in those eleven pages, but if he did, I missed it.
Blass-Debrunner-Funk, Greek Grammar of the New Testament and Other Early Christian Literature (University of Chicago Press, 1961), pp. 21-22 = § 39.3 (see esp. on p. 22) have an extremely brief discussion of OP's interest, and having noted the aleph/chi relationship in both Sira(ch) and Akeldama(ch), they comment: "Unusual". Pithy.
It would seem to imply a guttural pronunciation for aleph here, which is odd, since certainly by the evidence of the Dead Sea Scrolls it is fully quiescent, and the stronger ayin is headed that way as well. (On the other hand, ayin can be transliterated by gamma, which is some evidence for its pronunciation around this time.) However, this runs completely counter to the abundant evidence that aleph -- always the weakest of the gutturals -- is thoroughly quiescent at this time; see, e.g., P. Joüon & T. Muraoka, A Grammar of Biblical Hebrew (Rome: 2006), pp. 82-82 (§ 24) for full discussion.
The strangeness of these two isolated examples has attracted some attempts at explanation, including along the lines suggested by OP (that the "X" is a Hebrew aleph making an indeclinable ending for the Greek name). The fullest discussion I'm aware of is: Robert J. North, “The Qumran ‘Sadducees’,” Catholic Biblical Quarterly 17.2 (1955): 44-68 (discussion on p. 54). But there is no agreement about this, and all suggestions are speculative, and lack compelling evidence. There is certainly no other linguistic evidence or consideration which would explain these cases.
That discussion is a little rough and ready, but one at least should not generalize from OP's two examples to a more widespread pattern. I know of no other cases of Greek χ "representing" Hebrew א as we have it in these two cases.
Aleph and chi are "drawn" quite differently. Aleph takes three distinct strokes; chi is much more like a simple
X. Here are examples (from a roughly similar time/milieu) of aleph from the Great Isaiah Scroll (1QIsaa), the other showing chi from the Greek Minor Prophets Scroll from Naḥal Hever (8HevXII gr):
- = 1QIsaa, Col. 28, line 7 = last two words of Isa 34:6
- = 8HevXII, Col. B2, line 12 = LXX Zech 9:3