I propose the following:
Paul was converted/called on the road to Damascus. He visited the city, but soon left to preach in Arabia, where there were no other Christians. He made disciples but, having got into trouble with Aretas's administration, he returned to Damascus with some of those disciples. The Jews conspired with Aretas's governor to try to capture Paul, but he escaped with the help of his disciples.
Paul visited Jerusalem after his stay in Arabia and Damascus (Gal 1:15-18). Acts 9:26 tells us that the believers there doubted that his conversion was genuine. He cannot have preached for an extended period of time in Damascus or made converts there because the news of this would surely have reached the Jerusalem church via the Christian network, and they would not have doubted him. Therefore the converts that Luke mentions in Acts 9:25 must have been acquired by Paul in Arabia, not in Damascus. This is confirmed by the strange phrase, "his disciples". Converts in Damascus would have belonged the the church there and would not have been called "his disciples". I have benefited from Mark Goodacre's astute observations on this phrase but I disagree with his conclusions. The phrase makes perfect sense if these people were converted through Paul's solo preaching in Arabia. Gal 1:17 also supports the view that Paul had no Christian associates in Arabia, since Paul's purpose here is to explain that he had no opportunity to inherit his gospel from anyone.
We then have three silences to explain: Acts does not mention
- the conversion of the "his disciples"
- Paul's visit to Arabia
- The role of the ethnarch of Aretas in the plot against Paul (2 Cor 11:32-33)
The simplest explanation is that Paul had got into trouble with the civil authorities in Arabia. It may well have been illegal to preach in Arabia, for this would explain why there was no existing church there. In any case Paul's trouble with the authorities in Arabia explains why Aretas's ethnarch wanted to seize him. It also explains Luke's silences. It is well known that Luke down-plays conflicts between the church and the civil authorities. While it is often assumed that Luke wanted to convert those who were loyal to the empire, I think his motive was different. He knew that his text could easily fall into the hands of the civil authorities, so he had to be careful not to write anything that could be cited as evidence that the Christians were trouble makers. In any case, Luke's silence about Paul's stay in Arabia, the conversions there, and the conflict with Aretas's ethnarch are fully to be expected if Paul's activity in Arabia had been deemed illegal.
It cannot be proved, but I suspect that Luke, and much of his intended audience, were fully aware of Paul's visit to Arabia and his conflict with the authorities there. This would certainly explain why Luke includes the phrase, "his disciples". The difficulties associated with the phrase disappear if Luke expected his audience to know about the controversial visit to Arabia.
Other similar silences in Acts
As I argued here, the Jews in Achaia, in collaboration with the Roman authorities, had Paul's collection declared illegal. This explains why Acts does not mention it.
By combining information from Acts and Paul's letters we can infer that Jason was a believer who got into trouble with the politarchs in Thessalonica, and that he persisted in his support of the church (probably after being forbidden from doing so). Luke, however, was understandably reluctant to spell this out. He was therefore silent about Jason being a believer, and he calls him by his other name, Aristarchus, when he mentions him subsequently (see here).
Similarly, Luke does not reveal (to informants) that Gallio had approved the beating of Crispus. Instead Luke uses Crispus's new name, "Sosthenes", thus baffling his unintended audience.