As in this example:
ルイスさんの日本語は太田先生も外国人だと気づかなかったほど上手です。
I think that the beginning says: "As for Mr. Lewis's Japanese, even Prof. Ōta..."
And then the end is: "...[his Japanese] is so good to the extent that he [Prof.] didn't realise."
But did he not realise "if he was a foreigner", or that "he was a foreigner" just enclosed with the と particle?
Can 「気{き}づく ("to realize")」 be used with the quotative 「と」?
Yes, it definitely can.
Why so? Because in Japanese, the quotative 「と」 is used with far more verbs than English-speakers might associate with upon hearing/seeing the word "quotative".
Those verbs include:
・言{い}う "to say"
・話{はな}す "to speak"
・聞{き}く "to hear"
・書{か}く "to write"
・思{おも}う "to think"
・感{かん}じる "to feel"
・教{おし}える "to teach"
・気{き}づく "to notice", "to realize"
There are many more. Crazy, isn't it?
But did he not realise "if he was a foreigner", or that "he was a foreigner" just enclosed with the と particle?
The latter. My TL would be:
"Lewis's Japanese was excellent to the extent that 太田先生 did not even realize that he was a foreigner."
If this helps, 太田先生も外国人だと気づかなかった ＝ 太田先生も『外国人だ！』と気づかなかった. If imaginary quotation marks seemed to make sense for the word/phrase right in front of 「と」, you could be sure that it is the quotative 「と」.
In other words, 太田先生 thought that Lewis was a native Japanese speaker.
