Building natural language processing systems for non standardized and low resource languages is a difficult challenge. The recent success of large-scale multilingual pretrained language models provides new modeling tools to tackle this. In this work, we study the ability of multilingual language models to process an unseen dialect. We take user generated North-African Arabic as our case study, a resource-poor dialectal variety of Arabic with frequent code-mixing with French and written in Arabizi, a non-standardized transliteration of Arabic to Latin script. Focusing on two tasks, part-of-speech tagging and dependency parsing, we show in zero-shot and unsupervised adaptation scenarios that multilingual language models are able to transfer to such an unseen dialect, specifically in two extreme cases: (i) across scripts, using Modern Standard Arabic as a source language, and (ii) from a distantly related language, unseen during pretraining, namely Maltese. Our results constitute the first successful transfer experiments on this dialect, paving thus the way for the development of an NLP ecosystem for resource-scarce, non-standardized and highly variable vernacular languages.