If you’re getting an MBA, I’d say wait more than an internships length of time. Get a few years under your belt. In my industry MBA plus no exp = just a bit more pay for the same entry level position, but not enough to offset your incremental student loans (if applicable)
I work in planning, not marketing dept, but I am pretty familiar with how at least my company and parent company hire. Could be different elsewhere of course.
Main thing, I’ve interviewed people fresh outta grad school with little experience, and they sound just like the people fresh out of undergrad. Smart sure, driven, absolutely, but still no real world experience where I need it. Perhaps a bit more likely to get a call back, but that’s driven by not just the mba.