Yes, boutique consulting experience can be a strong foundation for MBB, especially when the work gives you real exposure to structured problem solving, client communication, and ownership of analysis.
The brand may be less immediately recognizable, so your resume needs to make the substance of the work clear. Strong bullets that show scope, impact, and client responsibility can help a recruiter understand why the experience is relevant even if they do not know the boutique well.
The advantage of some boutiques is that junior consultants can get meaningful responsibility earlier. If you can turn that into strong project stories and clear evidence of progression, the experience can be very valuable.
I would judge the boutique by the actual work and development environment rather than by whether the logo looks like a perfect MBB feeder. Good consulting experience is still good consulting experience.