This question is more difficult to answer than you probably realize. There has been a lot of debate about when precisely the camel was introduced to Egypt, but it seems clear that its primary purpose, from the earliest days, was as now: efficient desert transport. The animals were certainly known in Pharonic Egypt, as we have terracotta figurines depicting them from as far back as the dynastic period, and we have archaeo-faunal remains from the 2nd millennium BCE at least. When exactly the camel became a major player in the Egyptian economy is less certain.

They were associated with the god Seth, and so some suppose that early on their use as pack animals might have been forbidden. Others argue that it took a long time for the camel's use to be adapted to the irrigated Nile valley, but that they were always routine in the desert regions of Egypt. They were certainly the transportation of choice for the Arab merchant trains on the great Incense Route, which properly led to Petra and the Levant but also had spurs to Berenike (on the Egyptian shore of the Red Sea) and later to Alexandria, thence to the lucrative Roman markets of the Mediterranean interior.

Once the Macedonians take over in Egypt, their scribal tendencies lend a lot more evidence (namely papyrological evidence). Ptolemaic papyri rarely mention camels in any capacity, which would be strange if they were in widespread use. There should be records of sales of camels, for instance. There is plenty of anectotal evidence of their use at this time, but nothing that points to systematic exploitation of the camel as a resource. The simplest explanation is probably that there had always been some camels around, but not in great numbers, and that by the Ptolemaic period more and more were being introduced to Egypt via the Incense Route from Arabia.

In the Early Roman period in Egypt, traffic between the Nile valley and the Red Sea coast increased markedly, and the camel was the animal best-suited for that journey. Pliny the Elder details a route map from Koptos to the Berenike port city, mentioning watering installations (hydreumata) placed along the way (NH 6.102).

But as to your question: it is very unlikely that camels would be hanging around in Alexandria. They are not well-suited to humid conditions (like the Nile delta), and they do not do well when forced to walk through damp soil (their feet are susceptible to disease and damage like this). The are also very susceptible to annoying flies and the diseases they carried. Pliny mentions that the Arab traders smeared fish oil on their camels to drive away the gadflies.

So no, HBO did not have it right with the camels (technically).

For more on the camel in Egypt, along with donkeys and other beasts of burden, see the riveting volume by Adams, Land Transport in Roman Egypt (Oxford Classical Monographs 2007).