I did not even know you could do this, I will try when I get home.
Wen you drag/drop, it doesn't export the edits, just the original file? That seems a little counterintuitive.
Anyhow, you can set up presets in LR for exporting. That way you can standardize size/compression/format, etc. for exporting. The way I have it configured is I have a number of export presets, with different outpus (i.e. output for web, output for print, etc). When I r-click on the picture and select the export preset, it asks me where I want the file to go. Pretty easy. I even have an export preset that uploads the exported pics directly to my webspace.
Ruahrc