It is true that Hebrew, for a long time, was not a day-to-day language for mundane conversation, and modern Hebrew features a number of accents and variations of accents, including the “Yemenite” accent, the “Sephardi” accent, and the “Ashkenazi” accent. Pronouncing “ayin” like “aleph”, a glottal stop would be a feature of some modern Hebrew accents, but I don’t know which specific tradition(s) it comes from or how standard it is considered.
The Wikipedia article on Yemenite Hebrew notes, right at the beginning, that some scholars believe its phonology was influenced by Yemenite Arabic, while other scholars dispute that and claim that it was the other way around with speakers of Yemenite Hebrew developing a distinct accent speaking Arabic. So it seems that the development of these phonological traditions are not completely straightforward.