PRINTER: Status Checker

can I use the Arduino to check if a computer is sending data(to print) to any connected printer?

Depends on how the printer is connected (WiFi, Bluetooth, USB, Ethernet, serial, Centronics...)

the printers to be connected will most likely be through USB.
the plan is to use to ARDUINO to identify that there is a document queued
for printing.

to identify that there is a document queued
for printing.

Queuing will normally be done on the host, surely?

AWOL:

to identify that there is a document queued
for printing.

Queuing will normally be done on the host, surely?

By "on the host", are you asking if the arduino would be connected to the same computer as the printer?
If that is the case, then yes.

No, I'm saying that the queuing of the print job will normally be done by the host computer, on the host computer (i.e. the print job will be stored on disk), before the print job is transmitted by whatever means to the printer.

Marky_boy:
can I use the Arduino to check if a computer is sending data(to print) to any connected printer?

Conceivably you could insert the Arduino between the host and the printer and know whether there was communication between them, but understanding what the communication represented might need a lot of research.

I'm not sure what you're trying to achieve here, but if you want to look at the state of the printer and print queue then doing this from an application on the host PC seems like a far more sensible approach.