Yes, but it's not that simple. Probably the simplest kind of "displacement" reaction you might consider is SN2 - bimolecular nucleophilic substitution. I've neither the time nor inclination to give a full discussion of this reaction here, but two key properties you might consider (when predicting if this reaction would occur) are steric properties of the nucleophile and electrophile, and the 'quality' (for lack of a better term) of leaving groups in the electrophile compared to the nucleophile.
A thiol displacing a bromide ion would be an example of an element of lower electronegativity displacing one of higher electronegativity, but other factors are much more important - pKas, hard/soft acid base theory, steric effects, etc.