( Know-all mode on

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I am qualified and experienced in teaching English as a foreign language. Had Ola attended classes, she would have picked up the accent of the tutor, who would more often than not be local and, whilst made aware of it, would not have been trained to use received pronunciation ( i.e. the old school BBC accent) since it is not the accent students would encounter in most localities and settings.
In terms of local vagaries of grammar, certain local patterns they would hear would require explanation and often result in them being adopted by the student, largely to ease their everyday communication.
Also some pronunciation patterns differ in each language, so e.g. her difficulty with our" th" sound relates to the fact that it does not occur in the Polish language, it is the same for Polish people wherever they are.
In summary, chances are Ola would speak to some extent as she does whether she learnt formally or informally, the key difference being that she would probably have more awareness of other factors, and her reading and writing would also get more support as opposed to just her speaking and listening.
Bear in mind too that most non- native speakers don' t have their speech exposed on TV to a multitude of people each who have their own patterns of speech.