I would like to be able to drag bitmap images from my web browser into Inkscape. Is that possible?

I'm sure you have already tried it.
What I get when dragging e.g. from Firefox is a Bitmap Import dialog but if I press OK I get an Error Message.
So it seems like it is intented to work but for some reason (access rights(?) or Inkscape bug(?)) it doesn't.
Maybe worth filing a bug report?
For the time being you need to stick to:
1. Right-mouse-click on the image, 2. Copy graphics and 3. in Inkscape Paste with Ctrl+V.

What works on Mac is to drag the bitmap image onto the Inkscape app Icon in the dock - but will make a new document - no pasting into already open files afaik.

Cheers
P.

Maybe a two-step drag... keeps a copy locally, FWIW.

Doesn't work for me at all (except for the copy-paste option) on LM18.2, Xfce.

Copy/paste works here, sort of.
However alpha transparency is disregarded so ctrl+c/ctrl+v thumbnail from ocal with no backdrop leaves with a "black rectangle".
(win10 64bit)

I get the same result as TD, on Windows. Didn't try anything with partial or full transparency.