Depends on how large and complex the dependency is.
If the dependency is small and license-compatible consider bundling a copy of the files (a git submodule will end up being packaged as regular files in your crate). This way your package will build offline, won’t need to depend on curl/tar, and you won’t have to deal with complexity of failed and partial downloads.
If you want cross-compilation and other details of the build process to work, then
make alone is unlikely to work. You’ll need at least need to run
./configure with appropriate target.
OTOH if you avoid it and use
gcc-rs to compile sources it will handle most of Rust-specific concerns for you.
I don’t know about libseccomp specificially, but for a few libraries I’ve packaged the build process turned out to be needlessly complicated, and just giving all C files to gcc-rs, along with a few flags (copied from
make -n) worked out just fine.