Is upgrading to SharePoint Online/O365 easier from SharePoint 2013 on premise?

We have a fairly customized SharePoint 2010 on-premise implementation.  For clarity – our customization’s are:  SharePoint Designer Workflows, custom list input forms, custom DVWP’s, Nintex Workflows and Nintex Forms.

We are internally debating the benefits of upgrading our on-premise farm to SharePoint 2013, but we are also strategically planning to move to SharePoint Online/Office 365.

One question’s that we are struggling to get a clear answer on is:  will upgrading our on-premise farm to SharePoint 2013 be helpful (or even required) if our end objective is to migrate to SharePoint Online/Office 365?

Thanks for all feedabck!