LM317 µA Constant Current source possibility?

Yes, that is clever, I think it would 'work', however the problem is that Iadj is 50-100uA so that you will not be able to get an accurate load current. First, it is large, so your 200uA current might actually be 300uA.

Also, the temperature coefficient is fairly large:

And it varies with input-output voltage.

If you're looking to put a constant 200uA current through a grounded diode, there are better ways (even a resistor to a fixed 8V source would be better than the proposed circuit in several ways)

For example:

^{simulate this circuit – Schematic created using CircuitLab}