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.