I am developing an Task Pane Office Add-in using the Office JavaScript APIs in Visual Studio. When you run the application it runs in the desktop client version of Office.
There is now a new way to test add-ins in the online Office clients. You can directly side-load your add-ins by loading your manifest file into your browser storage. This is achieved by going to Insert > Office Add-ins and then selecting Manage My Add-ins > Upload My Add-in (on the My Add-ins tab in the upper-right corner of the dialog).
Keep in mind this won't be as seamless as using an Office 365 Developer site or developer tenant with access to the app catalog if you are using Visual Studio to do a one-click deploy + test, because currently Visual Studio doesn't utilize this side-loading feature. But if you don't use Visual Studio or don't want to use a dev site/tenant, this is an easy way to test your add-ins in Office Online.
Try it out and let me know what you think of this feature!