Time machine and firmware password

Hi all,

I purchased a used Macbook Air a few months ago and recently tried to reset the pram but could not proceed because a firmware password had been set. The original owner did not remember what he used so I took it into the genius bar and they removed it. However, part of their work required that they reformat my computer so I was wondering, if I restored my computer using my time machine backup, would that restore the firmware password?

Thanks in advance.