no, the angel gabriel couldn't possibly be the holy spirit. the bible identifies the holy spirit as the comforter, the spirit of god and the spirit of christ, and once again as indwelling believers etc. ---these are all things which aren't true of gabriel.
So, you're saying that because the Bible doesn't SPECIFICALLY spell out to you that Gabriel is the Holy Spirit, you are going to reject it entirely and call it impossible? :~)
Well, let every man be proven wrong and God be proven true!

I am going to test all of you again, and formulate here an argument that Gabriel is the Holy Spirit of the Bible:
I have been reading that Tertullian included the Book of Enoch as scripture? Apparently Jude quotes it, too? This is from Enoch 1, 40:8-9
8After this I besought the angel of peace, who proceeded with me, to explain all that was concealed. I said to him, Who are those
whom I have seen on the four sides, and who words I have heard and written down? He replied, The first is the merciful, the patient, the holy Michael.
9The second is he who
presides over every suffering and every affliction of the sons of men, the holy Raphael.
The third, who presides over all that is powerful, is Gabriel. And the fourth, who
presides over repentance, and the hope of those who will inherit eternal life, is Phanuel. These are the four angels of the most high God, and their four voices, which at that time I heard.
Sounds like it could be the Holy Spirit?
Another really interesting section comes from Enoch II. Enoch II is, of course, less supported by MSS. Many slavic editions exist. However, in 2009 coptic fragments were found of this later part of Enoch which date to perhaps 500 AD, most likely 900 AD. Check out this quote!
"And the Lord summoned me, and said to me: Enoch, sit down on my left with Gabriel." Enoch II, 24:1
So Gabriel sits at the Left hand of the Father, and Jesus sits at the right? Sounds like a trinity to me!
the bible identifies the holy spirit as the comforter
It also identifies him as Advocate, specifically in the legal sense. One who
convicts the world of their sin. I am reading that Jewish exegetes argued millenia ago that "Of those three, it was Gabriel who destroyed Sodom in a rain of fire (Gen. R. 50:2; B.M. 86b)."
This is from the Yalkut Shimoni (Jewish exegesis), which is only in Hebrew online. I suppose we would have to get a hard-copy in English to find out what their particular exegetical interpretation was. But, seeing as this was written by Hebrew-speaking Jews centuries ago, I must concede that they might see linguistic nuances that we don't :~)
Oh, and as for the comforter part, the Jewish exegetes have something to say on that, too:
He can also function as a guardian angel; he nursed the infant Abraham through his finger, protected Israel in Egypt, and aided the infant Moses (Yalkut Exodus; Sot. 12b).
Hmm, and aren't we told that it was the Holy Spirit in Exodus, too? This is just a thought..
Peace my brothers, May the Truth come.