edit...short answer ....Yes, you need an organizational account.
edit2... Late night, and I must have had appstudiio on the brain...but same goes for collector...
At the bottom of this page AppStudio for ArcGIS it has a link so you can sign up for a 60-day trial http://www.arcgis.com/features/free-trial.html?origin=appstudioforarcgis Given that info, and the general direction use of all the esri apps is heading, I would guess that yes, you would need an organizational account.
Are you able to get a named-user account in your organization? If not, at the UC they announced that "all software would become available with home use subscriptions" ArcGIS for Home Use Program | ArcGIS for Desktop Advanced for Personal Use What that really means I think is yet to be determined, but maybe it will allow for this to work. ??
This is nothing official, just speculation on my part. Since AppStudio is still in beta, there may be many changes before the final release.
EDIT:
Data requirements
To use your maps in Collector, you must have an ArcGIS organizational account. Your maps can include data from ArcGIS Online, Portal for ArcGIS, and ArcGIS for Server.
