I once ran into a 2 GiB limit with awk on a HP-UX machine. I think it depends on which c library it was compiled against. You can probably tell by looking for the 64 bit file IO functions in the binary:
strings $(which awk) |grep fopen
If you see fopen64, I think you should be OK up to files of stupidly large size. If you see regular fopen, probably you'll hit the limit at 2 GiB.