As per this link, https://dev.office.com/reference/add-ins/outlook/tutorial-api-requirement-sets?product=outlook&version=v1.5 Outlook Web add-ins work on Outlook 2013 desktop client and they also work on Outlook Web App (Exchange 2013 On-Premise).
Is it possible to get the add-in working on Outlook 2013 desktop client which has an email from the Exchange 2013 setup.
Yes it is possible for add-ins in Outlook 2013 to work on e-mails from Exchange 2013 On-Premise. However, the latest version of Outlook 2013 supports all our API's up to Requirement Set 1.4, whereas Exchange 2013 supports up to Requirement Set 1.1. Thus, if the APIs you need are supported by 1.1 and below, your add-ins should be compatible in both the desktop and web clients. If you are using APIs supported by Requirement Sets higher than 1.1, they won't work in the web client.
