I don't know if I understand this question. To make this concrete, here for example is an article about the discovery of an Old Arabic inscription written in the Greek Alphabet and a second Greek language inscription that nonetheless was written by someone with a "transparently" Arabic name and in the style of of other Safaitic (a variety of Arabic) inscriptions of the time and area. (Both almost certainly Arab nomads.)

Is your question whether historians would attribute both of these inscriptions to "Greek" people because they are in the Greek script and Greek language, respectively?

If that's what you mean, the simple answer is "no." Greek was the lingua franca of much of the Middle East for many centuries, and there is not very much more difficulty in taking a more sophisticated view of ethnicity vs. language among ancient writers than there is in later writers who, say, were ethnically Persian and composed their works in Arabic.

How these people might themselves identify is a complicated question as, yes, that was often connected with language and our own conceptions of identity, group, nation, etc. etc. are just very radically different from how ancient peoples would have thought about this. But you also have situations of bilingualism, and of communities that clearly resisted any kind of assimilation even in periods where there was probably quite a lot of bilingualism. For example, Jews who spoke Greek remained decidedly Jews even as others might have Hellenized.

There is a lot to discuss on related topics, but without knowing more about what you mean I'm not sure I would want to go much further down any particular path.