Yes, but also no. Firstly, there is nothing special about shotguns here, any gun follows the same basic principle, when fired a bullet is pushed forward, and the gun is pushed back with equal force. However guns don’t actually have that much total force behind them, bullets only move so fast because they are so light, so you aren’t gonna get much push. For example an AK-47 generates about 6 newtons of force per bullet fired. It takes about 10 newtons of force to lift a 1kg object.
xkcd that gives a better answer to a slightly different question (Is it possible to build a jetpack using downward firing machine guns?), and goes over the math better linked below.
[https://what-if.xkcd.com/21/](https://what-if.xkcd.com/21/)
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