Overpaying with Free overdraft

Hi All,
I currently have an arranged overdraft with my lender that by some mistake I don't pay any interest on. No matter how long I'm overdrawn for it costs me nothing.
With this in mind would it benefit me in using it to overpay my mortgage by an extra £500 a month?  I only have a few years left on my mortgage, would being overdrawn every month have an adverse effect on my future ability to get another mortgage after I've paid this one  up completely (5 years early)
Hope this makes sense 

Cheers S

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