I'm building a personal brand as an industry-focused research engineer ...

Meaning you're planning to run your own business.

What value can an MBA add to my career?

It might make it easier to assemble a successful business plan for your consultancy, but acquiring an MBA for that purpose alone might be overkill.

Will it enrich my career with management and business skills?

That depends. Are you anticipating that you may offer business as well as technical advice?