Getting the Message
I've written in the past about the libimobiledevice library and it's utilities. One, which is quite handy for gathering device information is ideviceinfo. It provides information such as the device description (color), device class (iPhone, iPod, iPad), device name, etc. When the device is unlocked, you can retrieve the serial number, as well. Basically, you retrieve the contents of the Info.plist.
But ideviceinfo is not so informative with a locked device. In fact, it won't show you any output unless you use the -s simple option. While you can obtain some information, such as the description, class, name, UDID (unique identifier), and Mac address, you can't display the serial number. But never fear, there is a way...
Linux has a system log that tracks systems events, included the plugging and unplugging of devices. The system log can be dumped the the terminal with the dmesg command. Run by itself, you dump the entire log and it's quite a lot of information to sift through, though in truth what you want will be found at or near the end of the log. You can shorten the output to the content you need with
$ dmesg syslog
But an even niftier trick is to set up your system to display the log as it is created and watch the output:
$ tail -f /var/log/syslog
This will display the last 10 lines of the system log and the "follow" it until you cancel with ctrl-c. Now you can hotplug your iDevice and watch the data that the system log records about the device. Unfortunately, you will see that it displays the device UDID and not the serial number in the "SerialNumber" field for a locked iDevice.
Recovering the Serial Number
The serial number is recoverable in Recovery Mode, however. Pressing and holding the hardware power button brings up the software power off slide button. Power off the device, and then replug it into your Linux box while holding the hardware home button. The device will boot into recovery mode. Now check your syslog with either of the two methods discussed above. Two serial numbers are displayed in the syslog after the product (iPhone, etc) and manufacturer (Apple) are listed. The first is the UDID, but the second includes several key:value pairs, one of which is the device serial number (key SRNM).
When you are done collecting the device data revealed in the syslog, reboot it, if required, by pressing and holding the power button approximately 10 seconds until the recovery screen goes blank. The device will then reboot into the operating system, probably feeling very ashamed of itself for revealing its secrets so readily.