Einstein's high international profile would have protected him, is it did Sigmund Freud, however he would have been dismissed from the German Academy of Science with the introduction of the Nuremburg Race Laws in 1935. It is important to note that, prior to the race laws, the only Jews being detained by the Nazis were detained for reasons other than their race; they were Socialists, Communists, trade unionists or outspoken critics of the regime. Jews sent to concentration camps between 1935 and the outbreak of the war were sent only for a matter of weeks or months, as a means of terrifying them into signing over their property to a German owner and fleeing the Reich, and as stated earlier; Einstein's international profile would have ruled that out: until 1938 the regime was very sensitive to international criticism.
Lise Meitner, the Austrian Jewish (by race: she'd been baptised a protestant prior to the rise of the Nazis) chemist and pioneering physicist had continued working at the University of Berlin right through until March 1938, protected by her Austrian passport. Following the Anschluss however, she was dismissed from the university. Despite Himmler declaring it undesirable for well known Jewish scientists to leave Germany in 1938 (because they were likely to spread anti-Nazi propaganda abroad), Meitner was still able to obtain a German passport (to replace her now defunct Austrian one) and leave Germany via Holland in July 1938.
If Einstein had been unwise enough to remain in Germany until the outbreak of war in September 1939, he would have been very unlikely to have been able to leave afterwards. Unlikely but not impossible as there were still routes out of Germany for Jews through until mid-1940, after which his fate would have been sealed.
