The Bible scholar Bart Ehrman has stated that he considers the Acts to be about as historically accurate as the Gospels. That is, that there is a historical core to it, but it is not history. This is the Bible book which the WTS uses to support the idea of the Christian congregation as a centralized, unified organization - and that is just what the author of Acts desired that the Christianity of his day would become. In such a work, the actual historical details can be thematized. For example, taking the miracle stories in the Gospels, it is likely that if Jesus was an actual historical person (and the a-historical approach has not so far been accepted by mainline scholarship), he did perform healings - but the examples in the Gospels may be likely stories rather than specific examples of those cures. In the same way, small scattered groups of proto-Christians may have experienced charismatic phenomena, and this is thematized by the story of the outpouring of the Spirit at Pentecost. This thematizing would include the large number of converts received even on that first day of the Church's existence. But, as narkissos has pointed out, this ignores the thought that the early Jesus movement was also found in Galilee - as indicated by the promise attributed to the risen Christ that he would meet the disciples in Galilee. The way Acts presents the movement as centered in Jerusalem is reminiscent of Isaiah's prophecy, that the word of YHWH would go forth from Jerusalem. (Isa. 2:3)
The statement in Acts 21:20, however, that there were thousands of believers among the Jews by the time James had his dealings with Paul - being a statement which, if historical, would have been made sometime in the 60's of the first century - is probably correct for the time it was supposedly made. This would be the case whether it is an actual recollection of a real conversation, or simply another literary device.
And just for the record, I have not made these statements as an atheist, but as a liberal Christian.