No, since the greeting is being made to him or referencing him as the leader

- he would not greet or reference himself


[Nazi salute - Description][0] 

> By autumn 1923, some members of the Nazi Party were using the rigid, outstretched right arm salute to greet Hitler, **who responded by raising his own right hand crooked back at the elbow, palm opened upwards, in a gesture of acceptance**.   
...  
The form "Heil, mein Führer!" was for direct address to Hitler.

The [German version][1] of the Wikipedia article also states:

> Hitler hatte den Gruß aber auch aus seiner österreichischen Heimat mitgebracht, wo „Heil“ als Gruß unter Freunden verwendet wurde – und in den westlichen Landesteilen noch heute verwendet wird...   
>
> Hitler had also brought the greeting from his Austrian homeland, where "Heil" was used as a greeting among friends - and is still used today in the western parts of the country...

So if Hitler did ever reply, he would have used the single word **Heil** in return. 

In the languages I am familiar with, someone, when being greeted, **does not** greet himself in return. 

A source that claims otherwise,  should be taken with a ton of salt. 


[0]:https://en.wikipedia.org/wiki/Nazi_salute#Description
[1]:https://de.wikipedia.org/wiki/Hitlergru%C3%9F#Ursprünge