Nice hypothetical, but apparently Judas simply did not do that.
From Gill's Commentary:
Act 1:25 - That he may take part of this ministry and apostleship,.... Of the ministry of the apostles, or of the apostolical ministration; which lay in preaching the Gospel, administering ordinances, planting churches, and working miracles; and which part, lot, or inheritance, Judas had; see Act_1:17.
And from which Judas by transgression fell; by betraying his Lord, whose apostle he was, he was turned out of his office, and had no longer part in the apostolical ministry:
that he might go to his own place; which may be understood of Judas, and of his going to hell, as the just punishment of his sin; which is commonly so called by the Jews, who often explain this phrase, "his place", by hell; as when it is said of Laban, Gen_31:55 that he "returned to his place", it intimates, say they (d), that he returned to his place, which was prepared for him in hell; and so likewise when it is said of Balaam, Num_24:25 that he "returned to his place", they observe (e), that
"he did not return from his evil way, but returned to his place; and so intimates by saying, to his place, that which was prepared for him in hell, as the Rabbins of blessed memory say (f); "they came everyone from his own place", Job_2:11 a man from his house, a man from his country it is not written, but a man from his place, which was prepared for him in hell; and because they came to show mercy to Job, they were delivered from hell, and became worthy of the world to come; and so here, and "he returned to his place", המוכן לו בגהינם, "which was prepared for him in hell".
And another of their writers (g), on the same passage, has this remark, and he returned to his place, and he does not say,
"he went on his way, for he was driven out of his way, and went down to hell.
And agreeably to what is said of Job's friends, the Targumist on Job_2:11 paraphrases the words thus,
"and there came a man, or everyone from his place, and by this merit they were delivered from the place, prepared for them in hell.
And which place the same Targumist on Job_8:4 calls אתר מרדיהון, "the place of their rebellion"; that is, procured by it: and so Judas's own place was what he had merited by his sin, and was righteously appointed for him; and though it was not peculiar to him, but common to all impenitent sinners, yet very proper for him, as a betrayer; for it is a settled point with the Jews (h), that
"he that betrays an Israelite into the hands of the Gentiles (so Judas betrayed his master), whether in his body, or in his substance, has no part in the world to come.
This clause is by some understood not of Judas, but of Matthias, or of him that was to come in the room of Judas; and by "his own place" it is thought is meant, the "part of the ministry and apostleship", in the former clause, and which the Alexandrian copy reads, "the place of this ministry", he was to take; and now Judas by his iniquity falling from it, made way for another, for Matthias to go to his own place, which God had in his counsel and purposes designed for him; or "into his place", as the Syriac and Arabic versions render it; that is, into the place of Judas, to take his place among the apostles, in his room and stead: the Alexandrian copy reads, "into that righteous place",
(d) Tzeror Hammor, fol. 43. 2. (e) Ib. fol. 127. 1. (f) Vid. Midrash Kohelet, fol. 74. 3. (g) Baal Hatturim in Numb. xxiv. 25. (h) Maimon. Hilchot Chobel, &c. c. 8. sect. 9.