DO NOT RELY ON COLOUR ALONE.
Status indicators should never rely on colour alone.
If you have any colourblind users (approximately 8% of people are colourblind) this will make statuses difficult to read.
Always accompany your status indicators with a meaningful/helpful symbol so that your users know exactly what the status means - Does it mean that a process has completed? Does it mean that an answer is valid? does it mean that a value is rising? etc. Help your users with that little extra layer of information
If you're using meaningful symbols then you can go back to using your brand green for success indicators because you're not just relying on the colour anymore ... and who doesn't want their brand associated with success, right?
EDIT for additional help:
Test your UI in greyscale - if it doesn't work then you need to rethink the way your using colour.