I found this on the Debian user forum, it appears the answer is yes and no:

http://forums.debian.net/viewtopic.php?t=7462

On 10/16/06, Leo Mauler <webgiant@yahoo.com> wrote:
The hplip page on the HP website says it supports the
Deskjet 3930, but when you try to use it the only
supported printers are the 3920 and the 3940, neither
of which seem to work as "similar" drivers.

Any other ideas to get this (admittedly cheap) printer
to work in Linux?

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