When you interview with a company, you are competing against yourself, not the other guy. A CFI may perhaps help you get an interview, but, you'll never know that. All you can do is work on making your resume as strong as possible.
I know people working for FedEx, UPS, DAL, CAL, and SWA who didn't even meet the minimums! They just happen to be at the right place, right time, and knew the right person.
-Fatty