The fp IDE uses its own internal compiler, not the installed command-line one, so it doesn't matter whether you install a cross-compiler.
If anything, you may try building a 64-bit IDE with it, but note that I'm not sure if it can be done. It it can be, it would be nice if you told us
Best of lucks.
Yes that can be done. I am actually always using it both on Linux 64 and Windows 10 64.
Simply:
make clean all install OS_TARGET=win64 CPU_TARGET=x86_64 IDE=1 GDBMI=1 PP=\the\path\to\bootstrap\ppcx64.exe
Given a 64 bit starting compiler or a 32 bit cross-compiler for win64 this will usually do the trick. The above compiles a full 64 bit FPC including a 64 bit textmode IDE fp.exe.
On Linux64 just change OS_TARGET=linux, change ppcx64.exe to just ppcx64 (and use a linux path /).
I am not quite sure if IDE=1 is actually still necessary, but it used to be and it doesn't harm to leave it in. This is a very old tried and tested recipe.
GDBMI=1 is the default in 3.2.0 so may also not be necessary. It requires a recent GDB, though. Higher than GDB 7.2. If for some reason you must use an older GDB, leave it out.
You can even build a 32 bit IDE that targets x86_64 (e.g. make crossall crossinstall IDE=1 PP=\a\32\bit\ppcrossx64) but it has been a long time ago I built such a beast. Not recommended.