I don't know how possible it would be, but I would love to see this feature.
Sync Deskpro tasks with iCal, Google Cal? - Community / Feature Request - Deskpro Support
Sync Deskpro tasks with iCal, Google Cal? Collecting Feedback
Zapier's a third party integration tool which allows you to link Deskpro to a mutitude of different apps:
You can install it in Deskpro from the apps section.
They currently run on a freemium model - simple integrations are free but to access more sophisticated integrations I believe you have to pay a subscription.