If you're running on Linux, use objdump --debugging. There should be an entry for each object file in the library. For object files without debugging symbols, you'll see something like:
objdump --debugging libvoidincr.a
In archive libvoidincr.a:
voidincr.o: file format elf64-x86-64
# Test whether debug information is available for a given binary
has_debug_info() {
readelf -S "$1" | grep -q " \(.debug_info\)\|\(.gnu_debuglink\) "
}