If it can support a 160 GB hard drive, that means its onboard ATA controller can recognize drives larger than 137 GB. Therefore, it should also work with a 250 GB drive.
However, assuming the ATA controller could not support a 160 GB hard drive, you wouldn't be able to partition it to get around the problem. You would be limited to 137 GB no matter how large the drive is, even if you partition it down.