So having tried to make the Arabs of Acts to be akin to Muslims, you ask this? No, not as defined by most of Judaism, which is liberal, or the traditionalists overall that evolved from the hardened Scribes and Pharisees overall whose father was the devil, and many effectively blaspheme the God of the OT.
But the devout Jews of Acts 2 did worship the God of the OT, the God of the Christians who, as did Saul/Paul "in all good conscience," which was not a god with a radically different theology than what the Christians preached, but Saul lacked fuller complementary, but not contradictory revelation, in contrast to the God of Scripture.
The question also can be asked, does Islam worship the same God as that the of OT, or even Jews today, and the answer is no. For once again, we are dealing with a religion overall, and V2 has affirmed Islam as worshiping the Christian God, yet the god of Islam is theologically clearly different than that of the Scripture, providing a competing and contradictory revelation, even to flatly denying that Messiah of the OT, and corrupting stories from Scripture, which the devil employs in his quest to acquire authority for his deception.
There is a critical difference btwn having some true light oe obeys, as Paul did, yet being ignorant of salvific revelation, versus believing in a false deity and gospel, which Islam teaches.
Thus while I am confident that there are some simple pious devout Muslims who sincerely seek the True God and will accept the revelation of Christ similarly, there are some simple pious contrite Catholics who lay hold of Christ for salvation amid the false teachings of Rome), yet their religion preaches "another Jesus," "another spirit," and "another gospel" yet V2 bears with him. (2 Corinthians 11:4)
And thus Islam does worship a false god, and just as so many of your traditionalists assert, V2 did affirm that Islam worshiped the same God as Catholics, and was wrong to do so.
The sections on Islam, Buddhism and Hinduism, tacked on late and rather hastily, were only a couple of sentences each. The whole thing was not seen as a full theological treatment, just a plea for mutual respect as leading to cooperation and peace amongst communities.
Some were saying that since it arguably broke with previous magisterial teachings, it could not be magisterial, for logical as well as theological reasons: A cannot equal non-A.
Others said it was not ever intended as a dogmatic statement but rather as a pastoral strategy: first establish and esteem the similarities and commonalities between Christianity, Judaism, and Islam. God is the Creator of all things visible and invisible, no matter who said it. Later focus on the differences/deficiencies of the non-Christian faiths. In other words: first connect; then correct.
It finally passed the bishops' vote on the rationale that it was not a change in doctrine, but a change in demeanor.
After it passed, it was swiftly trumpeted by its partisans as, yup, a wonderful overturning of nineteen centuries of doctrine.
A microcosm of the council, alas, and it remains controversial. And bait-and-switch may still be the modus operandi of Tio_Hagan_ Lio to this day.
That's why so many of us think he's a disaster.
I haven't really revisited this issue since I was a teenager. The most recent thing I read on it was http://www.ncregister.com/daily-news/nostra-aetate-love-muslims-how-do-i-do-that