Freshdesk's API V2 supports secondary emails during create/update a contact. other_emails attribute can support upto 4 secondary emails which can be associated to a contact. You can find an example here
Also now you can filter a contact using secondary emails too.
curl -v -u firstname.lastname@example.org:test -X GET 'https://email@example.com'
10 months ago
It's possible to update other_emails BUT the API is not capable of returning other_emails when using "/api/v2/contacts" (confirm by chat with your support team).
This is definetly a problem for synchronizing. Please fix.