This is a common perception, it's, however, inaccurate.

Did the Arab invasion of North Africa result in significant population change?

No!

are Arabs chiefly a genetic or linguistic group?

They can be considered both. I'll explain:

The Arabs conquest of North Africa was a gradual process, It happened over the course of about three decades. The conquests of Egypt started in the 640s, the Arabs were able to reach, modern-day, Tunisia, in the 670s where they founded Kairouan to serve as a garrison town. Around that time period, North Africa can be considered as being part of the Arab dominion. It's worth noting that the number of Arabs who migrated to North Africa was not larger than the number of Arabs who migrated to Persia and Central Asia. And that And that. The native population, the Berbers, rebelled. In 740 they defeated the Arabs in the Battle of the Nobles. It was the beginning of the end of the Arab rule of North Africa. The Arabs never managed to, successfully, bring the North Africa under their rule Several local kingdoms emerged afterwards. There were some Arab dynasties that appeared in North Africa, but their rule was over small territory, lasting for a relatively short period, and relying on the native North African to maintain their rule. This primarily sourced from Blankinship's The Reign of Hisham bin Abd al-Malik.

As for your second question, the Arabs traditionally were regarded themselves and were regarded as an ethnic group, with their own traditions and customs. With the large size the Arab empire (I use this term to refer to the single centrally ruled Arab polity lasting roughly from 632-756) reached, the traditional definition of "Arab" started to change. The subjects of the empire who spoke Arabic and had Arabic names, viewed themselves as Arabs. People not within the realm of the Arab empire tended to associate the term "Arab" with people who spoke Arabic or had Arabic names or were Muslims (associating Muslims with Arabs is still the case to this day).

In the past century "Arab" became defined politically, and the term became technical; "Arab" became defined as nationals of an Arab state (and Arab state became defined as state with a membership in the Arab League irrespective of the state's connection to Arabs or lack thereof). To give you an example of how the term is currently used, we can look at the nation of Sudan. Its name, as Ibn Khaldoun (a medievel Arab historian) notes, means "the land of the black people." Evidently, the Arabs in the Middle Ages did not view the people there as Arab, and this was true as the Arabs never ruled anywhere, roughly, south of the modern borders of Egypt. Sudan joined the Arabs league in 1956, its population consequently became Arab. Its southern part, in 2011, seceded forming "South Sudan." The population of South Sudan, who became Arab after Sudan was admitted to the Arab League, became no longer Arab in consequence. I'd like to note however that, there are people who are ethnically Arab, they're mostly based in the Arabian Peninsula and some parts of Iraq and the Levant. Greg Fisher's Between Empires devotes a portion of his book to the subject of Arab identity.

I think a comparison with the term "Irish" can further explain the paragraph above. Traditionally, "Irish" was used to refer to a specific ethnic group of the population of Europe. In modern-time, however, the term refers to those who hold Irish citizenship regardless of their race/ethnicity.