tl;dr: Kinda, but probably not really...

High-ranking Nazi's offices did have telephones, and they did use them to personally converse with one another - Goebbels mentions in his diaries congratulating Hitler on his birthday in 1944 over the phone, and he notes Hitler as being in direct telephone contact with generals in the East during Operation Bagration. It was in fact, a telephone call that led to the failure of the July Plot - Major Remer, commanding the Guard Batallion in Berlin had been ordered by the plotters to arrest senior Nazis based on their claim that Hitler was dead. Remer phoned the Propaganda Ministry and spoke to Goebbels, whose phone operator patched the call through to East Prussia, where Hitler spoke personally to Remer to reassure him that he was still alive.

Telephones in the 1940s almost always worked via an exchange, with an operator (usually women, but in military circles also soldiers or even officers at especially sensitive posts) literally plugging lines from one port to another to "connect" a caller to a recipient. In a high-ranking office like the Reich Chancellery or the Propaganda Ministry (since I'm relying heavily on Goebbels diaries for the mention of phones), that connection would then go to a secretary or the office of a secretary before being connected, or not, to the principal you had asked for at the exchange. That said, it was in principal fairly difficult to trace a call via a switchboard, as various forms of electromechanical switching were used in the background to connect the incoming call to the operators switchboard.

Further, as with many technological advancements at the time, Germany had a significantly less dense telephone coverage than some other similar countries. Whereas in the US there were 16.5 telephones per 100 inhabitants, and in the UK 7, there were only 5.3 telephones per 100 inhabitants in Germany in 1940. Telephones were also more expensive than in other industrialised countries - 2.5 times as expensive in real terms as France and 1.5 times as expensive in real terms as the UK in 1928. And while these got cheaper in the 30's, disposable income shrank during the Great Depression, so telephone use didn't become all that much more affordable in real terms. So even before the war, telephones were more expensive and less available than in other industrialised countries. What's more, a significant number of those telephones were in public places - be it phone boxes or the hallways of multi-family homes.

The war itself made telephone cals even less available for ordinary people, as the Wehrmacht, Air Raid Precautions and political leadership took up a large chunk of available connections.- After 1943 the phone system came under extreme strain from the effects of the Allied bombing offensive. A bombing attack on a city frequently knocked out the telephone network for significant periods of time after the raid, and once the connection was technically restored, the authorities needed most of the available lines and ordinary people wanting to speak to their surviving families clogged up the rest.

Finally, let's consider what happens if our theoretical practical joker overcame all these obstacles, found a telephone with enough privacy, convinced an operator to put him through to the Reichskanzlei and says "Nieder mit Hitler!" to the outer Secretary of Martin Bormann (Hitler's chief of staff). It may be technically difficult to catch him, but if he were, he faced significant penalties. As the war went on and the situation got worse for Germany, the regime's punishment for minor crimes deemed political became harsher. By late 1944, crimes which in 1940 may never have been reported or punished only lightly - listening to foreign radio stations; saying the war was a bad thing; being too friendly to slave labourers - were increasingly prosecuted as "Wehrkraftzersetzung", or "undermining the defence forces". This 'crime' was punishable by death, and thousands were hanged. It's not hard to imagine the fate of our prankster, denounced for not only speech that undermined the defence of the Reich, but sabotaging the telefone network - a critical piece of military infrastructure at the same time.

Sources:

An interesting source on some of this if you read German is a history of the German telephone system called "Telefonieren in Deutschland", published by the Max Planck Institut in the 90's.