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I agree this would be a good addition to Pandora. In the meantime, you can use 3rd party android apps like Scroball to connect your Pandora listening with Last.fm.
For the Windows desktop you can use Elpis for built in scrobbling. It is old and lacks some polish but does the job. I was hoping the Pandora client would support scrobbling out of he box. I'll stick with Elpis until it does.
Long since wished for this capability in Pandora. Will it ever be possible? Are developers looking at it? @TannerPandora do you have any updates to share?