the device you have defined, really is a diode conncted MOS transistor, since transistor is always in active region, noting I-V equation for a specified VGS=VDS=Device Vout, device has a different current value;
Since a current souce should have a constant current, Iout, for different Vout this device is not worth to use as a CS;
BTW, as you know, a CS must have large output resistance but this device for large amount of current output resistance is approximately 1/gm.
If answer is not very bad, it's not bad to help!
Regards,
SAZ