Hi Paul,
There's no direct integration between ArcGIS Online and Trimble Access.
There is the GIS Module in TBC that allows you to connect and Read data from a Shapefile, File Geodatabase or Enterprise Geodatabase (your organization needs the Esri Enterprise licensing to enable this).
You can use the Connection to convert the GIS schema to a FXL and work in Trimble Access, then Process the data in TBC and Write back the newly collected data to the GIS.
From the ArcGIS side you can then update your ArcGIS Online content (Web Map or Feature Layers) with the updated data etc.
There's the Blog on this here: https://geospatial.trimble.com/blog/gis-data-arcgis-geodatabase
And a Power Hour session link here: https://geospatial.trimble.com/blog/integrate-survey-Arc-GIS-data