Even though sodium azide is not a strong base, I still predict an E2 elimination. Hydrazoic acid has about the same acidity as acetic acid, so the result should be the same as treating with sodium acetate. Since the iodide is tertiary, an SN2 reaction will not occur due to the higher electron density donated by the methyl groups. That electron donation lengthen the C-I bond also. Lengthening the C-I bond increases the hyperconjugation of the C-H bonds (which are all equal). If they were not equal, then the more substituted would contribute more (more electron rich). This normally gives a Zaitsev product. In this case, they are all the same, so I predict an E2 elimination.
Because sodium azide is not as basic, I expect the reaction to be slower than a similar reaction in which a stronger base were present. None the less, I expect all other factors to be similarly applicable.
Now, since everything I've said is simply conjecture, I could be wrong. To answer this, it would be helpful if someone could look up this reaction (or similar) and post the results.