The answer to this question is no, the additional debug information is not loaded into the target memory when you download your program with the EJTAG probe connected to the debugger.
When you build a program with debugging, it increases the size of the elf file by adding additional information to debug sections in the file. But the text, data, bss and other loadable sections are the same whether you build with debugging or not.
The target memory use (size, location) should be the same for the program built with debugging and without debugging.
If you want, you can investigate the use of the mips-sde-elf-strip command. You can use this to strip debug and symbol information from the elf file you load onto your target. But you can still use the unstripped elf file to get symbols and debug information for the debugger.