Yes, this worked me for in the end. HOWEVER, in order to even see the option to post a shp zip as hosted service on AGOL one must have been granted publisher or admin status by an organization. I struggled with crazy-making app behavior for a whole day before I realized this (this will also unlock all sorts of analytical functionality on the map itself; plus you can make a map downloadable). Once turned into an admin, I could see this option. Here is the right workflow to do this:
1. I can't emphasize enough you need to become a publisher or admin in the organization. User will not do. See:
2. Create a new web map in My Content. Don't add anything to this yet.
3. Post the zipfile(s) containing the shapefile files as admin in My Content.
4. In My Content, edit each service file so that they are editable.
5. Go to the web map and add the now editable layers. Important note: I found out Collector will not fetch a web map if only some of the layers are editable -even if one isn't, the map won't show. This is why ALL layer components added must be editable. This is crucial but nowhere disclosed.
6. Go back to My Content, select the web map and the layers and share them with a group, if appropriate. You need to do this in My Content because only there (as opposed to individual layer or map sharing) is there the option to specify access and edit capabilities for participants (as opposed to just access). Note: sharing with a group implies you have already created that group and invited members prior.
Note the following doesn't apply to AGOL.
What's weird though, for 10 days before I was forced to troubleshoot this (my maps stopped showing in Collector suddenly), I had been able to post shapefiles normally (i.e. not as hosted services but as simple uploads) with user privileges and these showed in Collector fine.
Make sure your maps have an editable feature service. This feature service can be hosted in ArcGIS Online or coming from an ArcGIS Server. Then you can log back into the app or refresh the map gallery in the app.