Yes. The chosen undergraduate degree does not have much bearing on the graduate degree in this case so long as you have taken all required courses that stage you for an MBA first.
Your chosen alternative is one way to go. It is one alternative to fulfill upper division business courses given at the undergraduate level, which are sure to be needed, that you may matriculate in an MBA and if wanted, on into the DBA (Doctorate).
The MBA is a popular degree, and so a sufficient number of schools provide prerequisite in-class and on-line courses.
Not unlike students who do a pre-medicine track to become a doctor but major in a non-science, so does the principle apply to what you are wanting for the MBA. And so History is fine.
One might ask, What are the odds that a business major has better chances of getting in than a non-business major? Well, you have to ask advisors in business schools that question...
For example, students who major in Biology and Chemistry tend to have higher admittance rates into medical schools.
But unlike medical school, business school courses can be done on-line, whereas the majority of medical courses must be done in practical settings. And so the analogy to business that I draw here may be quite different.
