I'm not telling you to build GCC from source but Armory. If you insist on upgrading GCC, that's actually a complicated task on Debian. You'll want to look at the debian-backport repo instead, but I doubt they have a GCC recent enough in there.
I thought it would be a good idea to upgrade my offline signer to a current version. But I had to build from source because I need a 32bit executable (old Pentium M)
Compilation on 32bit x86 showed an error which was already reported for 0.95 - but the OP failed to respond to Goatpig's question about the build environment.
Check my response in that thread
https://bitcointalk.org/index.php?topic=1657365.msg20477795#msg20477795 if you run into compile error on "non standard" hardware.
Armory cannot build in 32bit on Windows atm, and I do not intent to do anything about it. The last native 32bit Windows is XP, and Microsoft themselves have dropped support for that OS some years ago.