Well, you're female, so that makes things easier for a start.
But, people get pigeonholed really quickly in this industry. Spend your first ever 2 days of work helping someone prepare for a process mapping workshop? You will forever after be doing process mapping for the rest of your life. Work on a project involving some IT stuff for a week? Prepare yourself for your certain career in IT. Accidentally stumble across a Partner who asked you to put together a few slides for a presentation? Congratulations, you're now a PA for the next 30 years. That's kinda how it works in reality.
Spend 1 year at ACN? Well... you're now an ACN calibre person. MCIM? Ideal for software sales roles.
You could do it I guess... but I wouldn't quit a stable job for it. Say you pass your GMATs... so what? They want a MBA or business degree, not GMAT.
Plus you'll be seen as 'damaged goods' in a way. Don't take this the wrong way, but I'm sure you know what I mean. They want people fresh out of university, who they can brainwash, um I mean 'train', in the way that they do things. They might be worried that, when they ask you to put together a powerpoint, you'll come back with a 30 page presentation full of slides with 4 bullet points at size 32 font each, rather than the powered-up all-night research packed quality stuff they're used to extracting from their keen-to-please analysts. For experienced hires, they basically only want rainmakers who can bring an order book with them, or possibly an old hand in a specialised field to plug a particular need for a particular project. They also tend to like it if you're well connected (e.g. the daughter of a senior exec at a FTSE company).
Plus, during a recession, I'm sure they'll keep up the interviewing (what else would the HR people do all day?), but will they actually be doing any hiring?
And not only that, but do you really want to get on that career path anyway? No job security, harsh appraisals, all-nighters, life out a suitcase etc?
The tier 1 firms can be great for some people, but my advise is to think long and hard before you quit a job for something that you may not want even if you do manage to beat the 200-1 odds and get an offer...