In the described situation, the person has performed all the physical actions required to become a Muslim. Another Muslim would ordinarily accept this person as a Muslim. Beyond that, it's impossible to be sure; it depends on the individuals heart, and is up to Allah.
It is plausible that not wanting to accept Islam (depending on what that means) is sufficient for that person to not have converted; it goes against:
That is because they disliked what Allah revealed, so He rendered worthless their deeds.
SunnahOnline ("Adapted from Tafsir Ibn Kathir") describes this as a kind of kufr (disbelief) called Kufr ul-Kurh (Disbelief out of detesting any of Allah's Commands).
Also note that there are different kinds of followers of Islam, and this may be applicable here too:
The bedouins say, "We have believed." Say, "You have not [yet] believed; but say [instead], 'We have submitted,' for faith has not yet entered your hearts. And if you obey Allah and His Messenger, He will not deprive you from your deeds of anything. Indeed, Allah is Forgiving and Merciful."
See also: What is a "Muslim" (surrendered) and what is a "Mumin" (believer/safe)?