Does identifying a student's sensory learning style and exploiting it result in significantly better performance?
I think your intuition might be correct. According to Hal Pashler, there is no real evidence for learning styles. The authors do not state that one particular learning style is applicable to everyone. Instead, they conclude that a particular subject may have a preferred learning style. For example, essay writing would have a preferred "verbal" learning style.

Source

Learning Styles: Concepts and Evidence by Pashler et al.Psychlogical Science in the Public Interest. Volume 9.3 (2008).