We just cannot know, unfortunately, what the average person thought of the Empire because we don't have good sources for it. They probably wold not have considered themselves to be "Roman" because at that time, "Roman" was a status conferred by citizenship rather than a purely national identity (you could be a "Roman" from Syria or Spain, for example, the orator Aelius Aistides envisioned the "Roman" status as being like a grant of "worthiness"). But I feel like the actual question you are asking is the broader one of would the average inhabitant of Roman Britain have felt themselves to be under an alien occupation, and that is the question we just don't have an answer to. There are bits of evidence from around the empire that seem to show anti-Roman sentiment, and bis of evidence that seem t show pro-Roman sentiment, but it is all too thin to make a conclusive picture.

However, from an objective standpoint, life was completely trasformed. Roman style pottery comes to dominate the pottery assemblages (pottery being the most visible archaeological material), urbanization transformed economic and social life, and the elites transformed themselves into a Roman character. There were certainly immense changes, it is just hard to know what anybody thought of them.