If by "real" you mean "spoken natively in the universe we know", then Dovahzul is not real. It is definitely not Hebrew. The entire dragon language was invented by the game developers at Bethesda Softworks.

The real language Dovahzul resembles most is English. How do we know this? Verbs do not conjugate, basic word order is SVO, there are definite and indefinite articles, and the roles of prepositions are basically identical.

On the other hand, dragon runes do bear a passing resemblance to ancient Mesopotamian cuneiform script.

Short answer: no. 

Long answer: no. 

It is a con-lang, a constructed language. Like Quenya and Sindarin (LOTR), Dothraki(Game Of Thrones) or Na'vi (Avatar).

Personally, I don't think that it is. There just aren't enough words in general for it to be spoken as a practical, real language.

I wish it was a real language, that would be amazing. Maybe once I am president of the world, I'll make that happen. 

It depends on how you define the language. If the language you speak refers to a communication tool, then I think Dovahzul is a real language because Dovahzul can indeed exist as a communication tool, and Dovahzul also has its own writing system and Specific pronunciation, so I think Dovahzul is the real language.