Indeed, just as French language and Latin-based orthographies for languages in this reason are the result of a colonial legacy, so too the use of Arabic as a prestige language (mentioned in this article) and an Arabic-based orthography.
Calling it an arab colony would be like saying Sweden was a roman colony because they use the roman script.
Sweden is not a particularly good example. A better example might be Latvia (or any of the other areas invaded as part of the northern crusades), which was invaded by a group of Catholics spreading the faith[1], Latvia could not be called a colony of the Papacy, but it certainly moved the area into Romes sphere of influence, with all the religion and language that entails.