Yes, with some printers, but it may be more trouble than it's worth.
For instance, modern workgroup printers with internal spooler and job
management tend to expose an interface to the job queue, so in principle
it's possible to write code to query the machine about the job queue,
identify the job and get its status.
Likewise if a local printer has a bidirectional interface and displays
its status on your screen when you print to it, it's possible at least
in principle to get the information.
But that's all I know. Getting the documentation for the interfaces may
be very difficult, though if the printer has a built-in http server and
a web interface for job management it should be possible to extract the
information that way.
