I figured out the solution for the issue.
Resolution:
To include qCascadingMenu programatically through a branding solution (VS, .NET Code) , do the below two things.
1. Add the below GAC assemblies in the reference.
WA.Core
WA.Common
WA.Navigation
2. Add the below in the Master page – top portion.
<%@ Import Namespace="WA.Navigation" %>
<%@ Import Namespace="WA.Common" %>
<%@ Import Namespace="WA.Core" %>
<%@ Register tagprefix="Common" namespace="WA.Common" assembly="WA.Common, Version=4.0.0.0, Culture=neutral, PublicKeyToken=2b4b09f1c57c8f0b" %>
<%@ Register tagprefix="Core" namespace="WA.Core" assembly="WA.Core, Version=4.0.0.0, Culture=neutral, PublicKeyToken=2b4b09f1c57c8f0b" %>
<%@ Register tagprefix="Navigation" namespace="WA.Navigation" assembly="WA.Navigation, Version=4.0.0.0, Culture=neutral, PublicKeyToken=2b4b09f1c57c8f0b" %>
Obviously you will be including the qCascadingMenu webpart XML in the required place in the master page.