Yes, if you were a Volksdeutsche or other person of German extraction.
The nazis attempted to start the Heim ins Reich (home to the realm) movement which aimed at both bringing Germans outside Germany (in Austria, Czechoslovakia and Poland) and the territories where they lived to Germany, but also convince people of German ancestry living further away to move to Germany. This included Volksdeutsche in Yugoslavia, Romania (Siebenbürgen), the Soviet Union, Estonia, Latvia and Lithuania.
Many of the Volkdeutsche had lived in their countries for hundreds of years and had been settled there either as a conquering upper and middle class (in the Baltic countries and parts of Poland) or invited as skilled craftsmen and traders or civil servants of the Habsburg Empire middle class (Yugoslavia, Romania, the Soviet Union and parts of Poland) and were often not very popular among the locals and thus receptive to the propaganda.
However, the German-speaking Swiss and the Luxembourgers proved to almost to a man reject the German propaganda, considering themselves Swiss or Luxembourgians before any German identity. Famously, in a 1941 census, 97% of the Luxembourgian respondents, when forced to chose between "German", "French" and "Other" as their ethnic identity listed "Other" and wrote "Luxembourgian" and added (in Luxembourgian German) "Mir welle bleiwe, wat mir sin" ("We want to remain what we are").
So, if you could prove German ancestry, you were welcome. If not, not so much.
To add on to /u/Vonadler's answer a little (even though my knowledge on this is hazy), some British sympathisers "made it big".
William Joyce (known as "Lord Haw-Haw") was (one of these big cheeses) a member of Oswald Mosely's "British Union of Fascists" from 1932 - 1937 in which time he'd become quite a big cheese within the organisation . He was a powerful & captivating speaker. He was praised with having the power of oratory.
In 1934, Joyce replaced Wilfred Risdon as the BUF's Director of Propaganda. Joyce was credited with shifting the focus of the BUF from corporatism to anti-Semitism & fronted the change of the BUF name to "British Union of Fascists & National Socialists". In '37 Mosley downsized the amount of people in the BUF-NS & unfortunately Joyce was made redundant, so he formed the "National-Socialist League".
A few months before WWII was declared, Joyce & his wife fled to Germany as he'd heard government were looking to arrest & detain him under Regulation 18B of the Defence (General) Regulations 1939 known simply as "Defence Regulation 18B or just "18B"; which gave the authorities power to detain suspected Nazi sympathisers, which in turn removed the accused's right to Habeas Corpus; The right to a fair trial by being brought forth to a judge, without this right you would just go straight from being charged to a prison cell. No innocent until proven guilty here.
Joyce & his wife became German citizens in 1940. When Joyce first arrived in Germany he couldn't find work, until he met with fellow BUF-NS colleague, Dorothy Eckersley. Joyce soon took on the position of broadcaster at the Reichsministerium für Volksaufklärung und Propaganda's ("Reich Ministry of Public Enlightenment and Propaganda") "Runfunkhaus"'s English service.
Even though the British were heavily discouraged from listening to Joyce's traitorous words, many did to hear about the propagated goings-on of Hitler's baby. That's all I can say on Joyce & his prescribed Haw-Haw persona. But I do have an audio clip of Joyce's last broadcast during the 2 month long "Battle of Berlin" (which always began with "Germany Calling, Germany Calling, Germany Calling".
Another alleged sympathiser is King Edward VIII, whom supposedly alongside his wife, Wallis Simpson visited Germany during the war & Hitler himself.
Sources & Further Reading
Mosley. O (1968); My Life
Dorril. S (2006); Blackshirt: Sir Oswald Mosley and British Fascism
Selwyn. F (1987); Hitler's Englishman: Crime of Lord Haw-Haw
Kenny. M (2003); Germany Calling: A Personal Biography of William Joyce
Benewick. R (1969); Political Violence and Public Order: Study of British Fascism
Farndale. N (2005); Haw-Haw: The Tragedy of William and Margaret Joyce
Morton. A (2015); 17 Carnations: The Royals, the Nazis, and the Biggest Cover-Up in History
"The BBC At War" documentary series presented by Jonathan Dimbleby.
Where are you emigrating from?