Been doing this for months, the 64-bit OS can run 32-bit apps with no problems as long as you have the required (32-bit) libs installed, see;
Code:
$ rpm -qa --qf="%{n}-%{v}-%{r}.%{arch}.rpm\n" 'firefox*' 'thunderbird*' '*libstdc++*' | sort
compat-libstdc++-296-2.96-132.7.2.i386.rpm
compat-libstdc++-33-3.2.3-47.3.i386.rpm
compat-libstdc++-33-3.2.3-47.3.x86_64.rpm
firefox-1.5.0.4-1.i386.rpm
libstdc++-4.1.1-6.i386.rpm
libstdc++-4.1.1-6.x86_64.rpm
libstdc++-devel-4.1.1-6.i386.rpm
libstdc++-devel-4.1.1-6.x86_64.rpm
thunderbird-1.5.0.4-1.x86_64.rpm
Your versions may differ, but all you need to do is install both the 32-bit and 64-bit versions of the libstdc++ rpm packages as shown above. One easy way is to download both versions and install them all at once, for example;
rpm -Uvh libstdc++*.rpm compat-libstdc++*.rpm --force
The force switch may be need because you may already have one version (32 or 64 bit) installed.