A directed graph is semi-connected if the corresponding undirected graph is connected

The following is a problem in CLRS:

A directed graph $G = (V, E)$ is semiconnected if, for all pairs of vertices $u,v in V$,
we have $u$ reachable from $v$ or $v$ reachable from $u$. Give an efficient algorithm to determine whether
or not $G$ is semiconnected. Prove that your algorithm is correct, and analyze its
running time.

I know there exist correct solutions to this using topological sorting and strongly-connected components, but I had a different approach.

My approach:

Construct a new undirected graph $G’$, having an edge ${u,v}$ whenever $(u,v) in E$ or $(v,u) in E$.
The graph $G$ is semiconnected if $G’$ is connected.
Will this method always be correct?