No, that's now how it works. Your team's current prestige does not have a direct impact/correlation with that jobs you are qualified for, nor should it.Think of it this way:
You took over a D- team, did a stellar job and are up to a C+.
Another coach took over an A+ team, stunk up the joint and is down to a B-.
Should the coach who's stunk up the joint be qualified for better jobs than the coach who's done great?
Qualifying for jobs is based upon your resume, not team prestige.