I have been unable to find the reaction anywhere on the internet so I'm assuming the answer is no, although I would like an explanation as to why. I can't seem to find any reason why it would not work, provided the reaction is carried out in two steps. In the first step, H2N:- will act as a nucleophile, attacking the least sterically hindered carbon of the epoxide. The second step would of course be an acidic workup. As stated in the question, I would expect the same exact mechanism as the reaction of Grignard Reagents with epoxides (substituting sodium amide as the nucleophile) due to the high basicity of sodium amide and Grignard Reagents. Like I said, I'm not expecting the reaction to be viable. However, I would like to know exactly why not. Im assuming it's something to do with the Hydrogen atoms of the amide anion, though I could be wrong. Enlighten me.
It actually is possible but it works well only with simple epoxides so it is not wildly used. $NaNH_2$ is extremely basic (it can deprotonate alkynes) and too many functional groups can react with it: alkyl halides (elimination), aldehydes, ketones...
To work around that basicity, sodium azide $NaN_3$ is commonly used instead, followed by the reduction of the azido group into an amine.
For example, see this article.