It's difficult to tell. With your background, I think you may already be pigeonholed as an account manager type. As a recruiter, I would be worried about your 'fit' in a strategy consulting environment. A lot of industry types think they would make good consultants, only to find out that their experience isn't relevant or high-level enough, and/or that clients expect polished deliverables and quite frankly the standard of literacy/structured thinking/ability to produce good quality written work isn't high enough (on average) from people who have become accustomed to getting things done by e-mail and on the phone. Do you have an MBA or experience in a professional services firm such as an i-bank or law firm for instance (i.e. anything but an IT services company)... this would help.
Personally I think technology consultants make good strategy consultants because they have quite logical ways of thinking, but a lot of people see it differently. For experienced hires, they seem to want people who are experts in a particular industry (FS, oil/gas, FMCG etc) rather than who have a functional expertise (e.g. IT) or who already have strategy consulting experience. For entry level positions, they seem to focus on academics and extracurricular activities, i.e. ability to learn/be shaped into their culture.
As an example, could you ever for instance imagine McKinsey hiring an account manager from Computer Associates and dropping them into a strategy assignment in the rail industry (as might be expected from any of their consultants)?