Considering that FEMA is an organization that relies on its head to provide direction, motivation, and leadership... Yes, I do think Brown's background was sufficient to lead that organization.
FEMA is made up of people who know how to do their jobs. What they need is not a micromanaging head, but a clear and motivating leader. The head of FEMA implements the policies of the President.
I've spoken with enough FEMA employees to have an idea of the organization.
But answer me this, did Brown do a competent job of handling past natural disasters during the time that he occupied the post? That alone should answer your question.
FEMA did a grand job in the Florida hurricanes of 2004. Maybe because Jeb Bush knew how to expedite assistance properly?