Does identifying a student's sensory learning style and exploiting it result in significantly better performance? Do people tend to have one pronounced sense (i.e., there is high variability in how strong the auditory, visual, olfactory etc. perception is among people)  and can
this sense, once identified, be exploited in both beneficial (e.g., targeted/adaptive learning/teaching) and manipulative (e.g., sales negotiations) ways?

My intuition doubts the effectiveness, but perhaps there is empirical evidence.
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).