So do an Export and "Add to Catalog" and "Same folder" with Photoshop as the Post Process action. If Lightroom doesn't see the changes after you edit, right click on the folder and click Synchronise.
Jpeg is lossy and lower quality. It's fine if you don't mind that information in your image is being thrown away. (It's a choice you make-I'm not making a judgement on your decision).
Still I wouldn't mind seeing it as a option for test images..