Only if you add an avalon slave (or custom instruction) to return the value from somewhere.Possibly you could set the 'cpuid' register (control register 5) to some useful value.
I used to do this to cook build numbers into the FPGA image so I could read it back if I ever needed to know what's currently operating in the FPGA. If you want something that you manually set once you can make a simple SOPC Builder/Qsys component that hardcodes the readdata line to whatever parameter setting you want. i.e. something like this:module serial_number_reader (clk, reset, address, read, readdata); input clk; input reset; input address; input read; output wire readdata; parameter SERIAL_NUMBER = 32'hDEADBEEF; assign readdata = SERIAL_NUMBER; endmodule Then when you instantiate it you type the serial number into it as a parameter and every time you read from the component that value is returned. If you want something more programmatic for a build system you can use an pre-initialized on-chip RAM where your build system spits out a new .hex/.mif file before the hardware is compiled. If you want a true 'serial number' system (where each FPGA/board has it's own serial number programmed at the factory) you'll need something programmable on the board that Nios II can read from with the serial number burned into it.