While it is not unheard of, I also think it is not the most effective way to enter MBB. Lateral hires are usually those who have been in the industry for a while and can bring their expertise in a relevant field to the firm. Lateral hires as BAs are candidates who under normal circumstances would have gotten into MBB (Target school, high GPA, impressive extra curriculars) but chose to pursue a different but equally prestigious path instead (startup founder/early employee, Investment Banking).
An alternative route might be to work in an industry of your choice in a role where you can build significant expertise for which there is a high demand in the industry. That can be leveraged to join MBB. You do not need an MBA to do this