No, but Spain's relationship with Nazi Germany is very complicated to say the least. From 1936 to 1939, Spain has a civil war which led to Francisco Franco as the head of government. He enacted a policy of strict neutrality initially, to keep out of the war initially. That changed when Hitler took over Paris and Spain switched to a policy of non-belligerence. Spain has intentions of joining the war, but did not fully join. Instead he aided Nazi Germany and Italy, to pay them back for the help they gave during the Spanish Civil War.

Spain was reluctant to join because of its heavy reliance on the United States which brought in a lot of trade. Spain was also still recovering both economically and in terms of man power from its civil war. Franco knew his country could not handle a full on allied attack. Yet Spain still got involved where it could.

Many volunteers, about 18,000, decided to fight with Nazi Germany on the Eastern Front. This group was known as the Blue Division and lasted from 1941 to 1944. Franco wanted to mantain peace with the UK and the USA, which is why the Spanish volunteers went to the Eastern Front. There were also many Spaniards that fled to France and fought with the French resistance. There were also a handful that fled to fight with the Soviet Union. Hitler wanted the British owned Strait of Gibraltar but Franco refused to let German troops on Spanish soil ending any negotiations on that front.

Spain, because of its poor economy at the time, relied on the Allies from trade. Portugal and Spain relied on each other, Portugal was helping Spain as much as it could. The US and UK were limiting Spain's access to trade, limiting how much it could get involved in during the war. If Spain fully joined the Axis during WWII, it would have likely destroyed its own economy.

By 1944, Spain switched back to a full state of neutrality. While yes, it did support Nazi Germany for a time, Spain also did not want to upset the allied powers it relied upon so it limited its involvement. Hitler did not try to negotiate with Spain by the end of the war. Spain switched to full neutrality by that point since it could see the end of Nazi Germany was coming.

Sources: Spanish Civil War: Spain's Great War by George Levrier-Jones (2013)

The Spanish Neutrality during the Second World War by Antonio Marquina (1998) - American University International Law Review - Volume 14 Issue 1

The Facist Reign in Spain by Steven C. Hause (2016)