I think that if you don’t have the fmc/pci adapter, then you won’t have any useful devices. Also, last I heard, the vc707 boot loader doesn’t support mounting the second partition on the SDcard. That just leaves adding the program to the initramfs somehow. Either by adding it as a formal package to buildroot, or by modifying the initramfs to add another file. I’ve never done this myself, but this site
suggests a way to do it.
If you are cross compiling, make sure that your cross compiler glibc is compatible with the glibc on the target. If they are different glibc versions, this is unlikely to work unless you static link.