Hypothetically, it's plausible, but here's the difficulty: All citizens were required to trace their lineage to their great-grandparents and prove they were healthy Aryans. If they had any relatives that were Jewish, they were considered either Jewish or mischling ("mutt"). So in order for your hypothetical non-practicing, ethnically ambiguous Jew to blend in, his whole family for generations would have to be the same - or he'd have to have a way to forge documents. It's not impossible, but I'm not aware of any examples. Maybe someone else knows!

There were a large number of Jews who survived the war under false documents and assumed identities. This was risky, since there was always a chance you'd run into someone who knew you before the war, or the forgery/deception would be detected, but it was possible.

Since you specified Nazi Germany, the issue in Germany is that Jews were required to register and lost legal rights during the 30s, well before the Holocaust began. The punishments for not complying were severe. At that point it was seemingly massively advantageous to comply. Once this occurred the German government knew who was Jewish (according to their metrics, which covered many people who did not actually identify as Jewish, and were not thought of as Jewish by the Jewish community), so if you were on the list they would know that you were Jewish. Plus, in some cases the Nazis were able to use pre-war records from governments and organizations to develop lists of Jews. This is partly why many Jews today are leery about providing their religion to census-takers, or non-Jewish organizations having any sort of "list of Jews".

In Eastern Europe, Jews were not as well-integrated into society at large as much as in Germany, so simply pretending to not be Jewish was not possible for most people. You can't really pretend to be Ukrainian if you don't speak Ukrainian (and many Jews in Ukraine would've spoken at least some Ukrainian, but not everybody, and maybe not well enough to pass as a native speaker). Plus you couldn't easily get up and leave to somewhere where no one knew you, so someone who recognized you would give you away. Here, again, there were compulsory registrations of Jews, and often the penalty for not showing was death. Of course some of these registrations ended in those who showed up being killed, but many Jews didn't think this would occur, or were in denial.

It was quite difficult and also involved a lot of luck. Because there were so many ways bureaucratically that Jewish identity was checked in the years before the mass killings began, there was generally a paper trail. And if you wanted to go underground (Jews who used false papers to pretend to be Aryan were called "u-boats"), you ran some risks in terms of being found out, your papers being found to be false and such. Those are more passive ways of detection--you make a mistake and someone notices. There were also active ways of detection. The SS blackmailed a few Jews into being "catchers"--Jews who, working for the SS, traveled around looking for U-boats. They could spot Jews they had known from earlier years, with the Jews thinking they were meeting another U-boat and friendly face. For example, Stella Kuebler (born 1922) was a Jewish girl living in Berlin. She lived a secular life with her family, until 1933 when the Nazis came into power. Her father lost his job when Nazis passed laws forbidding Jews from holding most jobs. Jews were also kicked out of public schools so they founded a Jewish schools for their children, which resulted in Jews getting to know lots of other Jews, regardless of whether or not they were practicing. Later, Stella became a "catcher" when the SS threatened they would kill her parents if she didn't. She could recognize many of the kids she went to school with and as part of her job traveled around Berlin all day looking for them and turning them in to the Gestapo. Peter Wyden was a schoolmate of Stella Kuebler and he had a big crush on her in school at that time. Later, he wrote a book about her. Wyden was one of the lucky ones and his family was able to get a visa to the US and thus escaped Nazi Germany. At the end of the war he returned to Germany as part of the US army psychological warfare division. He found out the truth about Stella at that time. Wyden says, anecdotally, that many believe that Jews who didn't "look Jewish"--who were blonde like Stella, with pale skin, rather than the more stereotypical olive skin, dark hair and eyes, and very curly hair--found it easier to successfully be a "u-boat" and evade detection. I know anecdotal evidence is frowned upon here, but there's no way to quantify this information and this is an anecdote from someone who grew up in Nazi Germany.

Plenty of other Jews tried to escape the Nazis, but it was a difficult thing because other countries didn't want to take in Jewish refugees. Hiding out with fake papers was never plan A.