Harold - I asked one of our ArcGIS Pro Add-ins instructor if this was possible and here is her comment:
"I haven’t tried it, but you might be able to set a property on the module that gets loaded so that it loads automatically instead of waiting for a button/control click: https://github.com/Esri/arcgis-pro-sdk/wiki/ProConcepts-Framework#jit-loading
The other option are Pro Solution Configurations. https://github.com/Esri/arcgis-pro-sdk/wiki/ProConcepts-Framework#configurations
Pro SDK team might have more thoughts…"
Hope this helps!