We have a large 9 gb TPK that we have been using with another mobile app. It has scale dependencies where when zoomed out it gives a topo and then when zoomed in it gives our own imagery. Works great in other app.
In collector I can side load it and select it as a basemap fine. But when I zoom in it never changes to the imagery. Stays with a now rather blurry topo. My web map is set to a basemap of imagery so I know it is using it, it will just not change when zooming.
You can only use one basemap at a time in a disconnected map in the Collector. The basemap you choose when downloading the operational data will be the one displayed in the disconnected map. We are working on improving this experience and bringing in the functionality of switching basemaps.
You could set up the Esri layer as an operational layer with scale levels at the bottom of the layer control and then have your other basemap ready on device and you can then use the custom basemap to define the extent and download the data. All tiled services being used however will need to be in the same projection which is Web Merc.