If I use 32bit PC to compile the image for my platform, can it run Laird SDK lib for MSD50NBT in Linux?

No, the toolchain Laird use for MSD50NBT in Linux is arm-laird-linux-gnueabi_3.5.2.8 and  it's 64 bit. So must use 64 bit PC and toolchain to compile the OS image in your platform, then it can link properly with Laird prebuilt SDK lib.