Is it necessary to be a Graphics Designer in order to successfully run
a Graphics Design Company? Is it unusual for a company to hire someone
to design for them?

My answer would be no. Of course, it would help, but shouldn't be
necessary. As for the second question, MOST people hire someone to
design for them. Certainly, people aren't often out there designing
their own logos and marketing materials. They hire someone to do it.
Now, if you mean EMPLOY as opposed to CONTRACT, then I would guess
that most people contract designers because they don't generally need
a designer full-time or permanently. Design work is generally on an
as-needed basis.