How to deal with questions having two or more asymptotic notations
No, this is not the right way to think about this question. To get you on the right track notice that $f(n) \in \Theta(f(n))$ no matter what. This should give you the right intuition. However, you can't prove equality with just one function taken from $\Theta(f(n))$ you have to consider an arbitrary function. 

If you work through carefully (I won't give you the step-by-step since active learning is important), you will see that $\Omega(\Theta(f(n))) = \Omega(f(n))$. To test your understanding after you figure this out, make sure that you can also show that $\Omega(O(f(n))) \neq \Omega(f(n))$.

The intuition you should keep in mind (that you have to make rigorous by carefully understanding this table) is that $\Omega$ is kind of like $\geq$, $O$ is kind of like $\leq$ (for lower case of both, make them strict inequalities), and $\Theta$ is kind of like $=$. But this is only heuristic intuition. Make it precise on your own, and see if you can find any weird functions that might serve as counter-examples.