In most fields, I think the research indicates the opposite, though I don't know of any research that is directly on point.
One of the weaknesses of multiple choice tests is that they allow the student to write the answer when they recognize it among the choices. This is easier than retrieving it without answer cues, and so the well-established benefits of retrieval practice (a.k.a. the testing effect) for retaining information aren't gained. However, in math, even multiple choice questions typically require some calculation rather than mere recognition, so this is likely less of an issue in math.
While I don't know of research directly on point here either, I also suspect that multiple choice tests give students an excuse to guess on a problem and stop thinking earlier than they might if they had to come up with something rather than leave a free response question blank. Since even unsuccessful initial struggles with a problem promote retention (assuming appropriate feedback is soon provided), I would imagine that this would be a problem even in math.
Also, while very skilled test writers can find ways to write test questions to test a wide range of thinking processes in math, it isn't easy. Even some government or commercial sources often produce multiple choice questions in math whose intent can be evaded by a clever student. (A blatant example: figuring out which choice is the solution to an equation by plugging each choice in turn into the equation rather than solving the equation.)
As for anything that indicates superiority of multiple choice questions in some respect, I don't know of any. They're really used more for convenience than because they're better at promoting learning.