Is it possible to view the file only, but not downloaded?
It depends on the application you are using, file format and how the file get uploaded to Trimble Connect. If you are using Trimble Connect web application, you can click view the file that has been uploaded and has completed assimilation process on Trimble Connect project without having to download to local drive.
However, if you would like to view the model through Trimble Connect desktop or mobile application, then file need to be downloaded on the apps before viewing the model.
Would you mind letting us know which application you are using?
check attachment for clarification.
The read-only folder permissions allow users to click view and download the file but users would not be able to update that file on Trimble Connect. You can share the model and allow users who is not a member of the project to have view only access using "Share Data" feature (the third button next to the download icon in your screenshot). However, this feature will not include Open in SketchUp viewer app button on the page and it is available for users to view the model in Trimble Connect 3D viewer app only.
Retrieving data ...