Does McKinsey still hire Business Analysts a year or two after they graduate?
Yes, they do though it is less common.
It typically happens if someone took the time to get a masters degree that is not an MBA. In many cases, those graduates, especially if they do not have work experience, would be guided toward the Business Analyst track rather than the Associate track which is targeted around MBA, JD, PhD, MD degree holders and/or those with many years of work experience (say 5+ years).
Other exceptions - if someone spent two years in the Peace Core, doing a Fulbright scholarship or some other kind of "weird" but highly respected opportunity.
In terms of coming out of working somewhere else for one to two years, that's much less common. I'm not aware of any policy against the hire, the main issue is it's much harder to get an interview, because the firm is not setup to seek out and recruit candidates with this background.
For a candidate with one of those weird experiences, their resumes stick out (in a good way). With just one or two years work experience elsewhere, it's much harder to stick out.
So practically speaking, your entry points into the recruiting process are: a) networking to find someone internally who will get you an interview (after which if you are good, it's a possibility... the firm hates to turn down exceptionally talented people.)
You will also want to time it such that this takes place before the main on-campus recruiting and offers go out. It is much harder for them to make an exception after they just sent out a bunch of offers and internally feel like they are "done" until next year.
I'm not 100% sure on this last point, because a secondary issue is figuring out when your start date would be. Most BAs start around the same time so the office can do training all at the same time, etc... So in some respects, there is not perfect time to interview.
If you do it right before offers go out to on-campus candidates, then the prior year's class has already started their first day of work. Would they give you an offer and ask you to start nine months later? That's kind of weird. Or would they ask you to start right away (but then you are off-cycle)?
So expect these issues to potentially pop up. And expect a natural reluctance on the part of someone internally to want to deal with all these issues. So bottom line, you need an advocate internally who will get you an interview, and you'd better be darn good when you interview.
And I do think the bar is a bit higher to have someone internally go through all this extra work just to bring you on board.
That being said, it is possible, but definitely not easy.
b) Your other much more natural entry point is to get an MBA and apply on campus then. Many people have pulled this off, successfully getting an Associate offer after an MBA when they were unable to get a Business Analyst offer before the MBA.
This is because the Associate recruiting process at McKinsey is less competitive than the Business Analyst role. The core consultant role at McKinsey is the Associate role -- so they hire a lot of them (relatively speaking anyway).
In comparison, there are far fewer BAs hired in any given year. Internally, BAs are considered by many to be the most impressive analytically of new hires.
The second year BA is considered the perfect person to staff on a project -- they outperform first year Associates by a wide margin, and they usually bill out at less (so a partner can squeeze a second year BA onto a project with a tight budget, whereas an Associate might not work).