There is research about so-called "human calculators" who do mental math with large sets of figures; in every instance these folks have developed their talent by spending countless hours memorizing arithmetic facts and relationships. Seems in the most extreme cases their brains are wired to support this sort of activity.
http://rstb.royalsocietypublishing.org/content/364/1522/1385.short
However, if we are talking about whether mass memorization equates to meaningful learning for the typical person, evidence from the 1950s demonstrated this was not the case beyond the retention of simple facts:
http://www.sciencedirect.com/science/article/pii/S0022101507632996
Learning with connections is far better. Think about early school mathematics books (in the 1700s) that had page after page of formulas to memorize related to commercial transactions involving proportional relationships among different units. The time and effort it took to try to memorize these was inordinate (and drove many away from mathematics). More "modern" textbooks by the early 1900s had students learn about proportional reasoning as a general relationship that could be applied to an infinite number of specific situations - thus by learning one conceptual relationship (which could then be memorized and also re-constructed if learned with understanding), students had a much better chance of both long-term recall and correct application.
Some recent articles related to this idea demonstrate quite powerfully the advantages to conceptual learning.
http://onlinelibrary.wiley.com/doi/10.1002/ddrr.45/pdf
http://www.academicjournals.org/ERR/PDF/Pdf%202011/Jan/Narli.pdf
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