For future reference, it's worth noting that while Rock, Ground, and Steel types don't take damage from Sandstorm, only Rock types get the Sp. Def increase. Regardless, upon doing some Showdown testing, I can conclude non-Rock Tera negates Sandstorm's Sp. Def Boost.
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As you can see in the image, Tyranitar would normally get an increase to its Sp. Def, though as it's terastalized into a Dragon type, it does not gain it, while also still taking damage from Sandstorm. This is also the case for other methods of changing type, such as Soak.