Yes—Lightroom can be set to apply sharpening automatically on import by changing the default Develop settings, so images will appear with that sharpening whenever they load. You can adjust the default sharpening amount from the Develop module via the default settings option.

Also, if images look unusually soft while reviewing, make sure Lightroom has generated Standard or 1:1 previews in the Library module; otherwise you may just be seeing lower-quality previews.

The downside is workflow-related: sharpening is generally best treated in stages, with final sharpening done last. Over-sharpening early can mislead your editing decisions, especially before other adjustments are finished. A common approach is light capture/input sharpening early, then creative sharpening during editing, and output sharpening at export/print.

So: yes, you can apply default sharpening for easier culling, but keep it modest and don’t treat that preview sharpening as your final sharpening.