I know someone that is studying ACA and working in a management consulting firm. The requirement for ACA is that you need to have accounting experience. Whilst saying that, accounting experience is a broad term and does include 'consulting'. Accounting is the foundation of any work that involves a business and therefore, it can be applied.
However, as consulting firms are generally not registered to have their employees study ACA, I think there could be requirements for you to apply for a special case and just have to explain how your consulting job relates to accounting experience (e.g. financial statement analysis, strategy, budget accounting, KPIs, balanced scorecard etc - these are all studied as part of the ACA)
Just a note though, it's going to be tough working in consulting and studying ACA at the same time! Good luck...
This is my understanding but someone please correct me if I'm wrong