It clearly depends on what kind of future research you want to do but a lot of MBA content will not be relevant to anyone who will manage a non-profit lab, although it might help with the business of running a lab (e.g., a for-profit lab).
Here are just some examples:
- business environment: Here you are going to learn about international trade, competition, etc. and how those impact competitiveness of a company. I don't see how this will help you run a lab unless your lab is operating in competition with other labs for customers (or other constrained resources).
- accounting: Here you will learn about creative ways to maximize your organization's profit leveraging tax law. I believe most labs are non-profit and, thus, I do not think creative accounting is an important skill (but I might be wrong here).
- business law: Here you will learn national and international laws which can impact trade. You would naturally learn about contracts, negligence, and other related topics. This might help you understand what makes a valid contract or what the impact is of leaking private data but I am not sure it will help you much other than avoiding being tricked when someone says 'I will fund you if you just sign here.'
- human resource management: Here you will learn about how human resources add to a company's profitability and how to plan for them. The focus will generally be more strategic in nature and could help you do some strategic planning. One such issue is 'employer branding' and clearly you do want people to want to come to work for you. This might help you but as you are smaller, the benefit will be smaller.
- finance: Like other modules, the focus here will be on strategy. How do different funding sources, and different balances between sources, impact profitability by minimizing your cost of capital. Non-profits have a much more limited choice in their sources of capital so this will be of very limited use for you.
Normally, MBA programs do include a thesis which includes research. This clearly can tell someone if they want to do more research and it will give them some research skills.
Now, there is (hopefully) going to be a change in the way the student thinks. That is, students should think more strategically. This skill (strategic thinking) should give you a benefit in most things you do in life by encouraging you to think more long-term.
All this said, if you want to start a for-profit venture which focuses on research (selling your output) then, yes, an MBA would be quite helpful. However, you should not think an MBA is about managing people better. It is about that but it is much more about how to maximize your profits through maximizing your revenue, minimizing your expenses.
If someone is going to run an academic lab, I would encourage them not to take an entire MBA (unless they really want to think like business people) but rather take a class on a subject where they want to be stronger (e.g., human resource management).
EDIT: I think Edward's answer is good but to go a bit further about project management courses, this might actually help a researcher, especially if that research is managing a team.
In project management courses, you would learn about different topics than an MBA. For example:
- Feasibility studies
- Planning, organizing, controlling (general management issues)
- Reporting progress on your project
- Risk management
- Change management
- Leadership, motivation, human resource management
- Several others
Because most research is a project (has a start date and an end date, has resources including people and money, etc.) this could be much more suitable (than an MBA) to someone leading a lab. I would recommend starting with a single project management class (which will generally give you an overview of each topic) then, if you want to really dig into more detail, consider getting a master in project management or perhaps an industry certification like PMP.