Not "more". Influenced, that's all. Jallad et al. want that it be genuine from Arabs Nabatean script because they want absolutely nothing of foreign to "Arabs" ; Islam must be genuine Arabic .
I agree that seeing this gradual evolution from Nabatean to Arabic is far fetched.Of course it is. But they say the contrary, for them it is granted! the Quranic script is coming from Nabatean script, end of story.
But the "transition" they do not explain it. From where it comes? From Heaven, like the Quran? Hahaha!
All the North Arabic script (which are clearly just before the Quranic script) inscriptions we have from 470 to 568 are under the cultural sign of Christianity whose the script is Syriac.
But the Quran is Arabic? Aaron is Arab? Jesus is Arab? Moses is Arab? Abraham maybe? (Hahaha!)
Listen to Guillaume Dye (in French!) :
https://youtu.be/XELIg_Aycm4