Reaction of secondary alcohol with ammoniacal silver nitrate (Tollens' reagent)
This question refers to the use of Tollens' Reagent (ammoniacal silver nitrate). The oxidising species here is the diamminesilver(I) complex $\ce{[Ag(NH3)2]+}$.

Tollens' reagent is usually used as a test for aldehydes, with which it gives a characteristic silver mirror: 



It is often said that Tollens' reagent does not react with alcohols. However, from personal experience, gentle heating of a primary alcohol with Tollens' will cause a small amount of oxidation and result in a fine black precipitate. Again, in my experience, secondary alcohols (such as in the question) do not react with Tollens' reagent and so I would predict that no reaction will take place here.

EDIT: Your proposed mechanism certainly looks plausible but whether it will take place in reality I can't say for certain (my experience of Tollens' reagent says no).