Tommy- Yes and No. GeoForm is a javascript web app template that is fed by a web map. That web map could come from a portal instance hosted on premise by your organization. As you may now, starting with ArcGIS Server 10.3, all on-maintenance server licenses come with Portal for ArcGIS as well as a number of named user accounts (depending on your server level). So you will need Portal to run GeoForm, but you will begin to get Portal free (10.3 is prerelease in Sept. and officially released in Nov.) So you won't need ArcGIS Online to use it, but you will need to set up a Portal for your organization. Does that make sense?
Chris