I don't know what you mean by the "Lightroom Gallery tab". However, I just verified with LR CC and Windows 8.1 that if you drag a pic from File Explorer into the center of LR Library Grid mode (do View > Grid), the import is invoked.
Which version of Windows do you have?
With Gallery i meant Library, my mistake (wrong translation, i am using the german version).
What works with your setup doesn't work with mine.
As you can see (cursor) i can't import the file from the file explorer on the right.
(The file is not already in the catalogue and i am in the library tab grid view mode).
Using Windows 7 x64 prof Service Pack 1
Hmm, perhaps the difference is Windows 7 versus Windows 8.1. Hopefully someone else who has Windows 7 can see if the problem also happens on their system.
Reinstalling didn't help and deleting the preferences file didn't help either.
Is there some adobe employee active here, or are they just trying to outsouce support to other users?
Adobe doesn't participate much in this user-to-user forum. You can try posting on the official Adobe feedback forum: Recently active topics in Photoshop Family about Photoshop Lightroom. Adobe does read all the posts there and occasionally responds. I wouldn't waste your time with trying to call or chat with Adobe support.