I would be less concerned about the use of the LED as a voltage reference than the fact that a current source won't work if the base bias circuit is connected in parallel with the transistor. To be specific, if you want to use that circuit to source current from the positive rail, you have to use the PNP version of the circuit, so that the base bias resistor can be connected to the 0V rail and the LED current path is independent of the path of current into (or out of) the collector of the transistor.
Have a look at the NPN version of the constant current source (sink). The current is sunk into the collector, and the base bias circuit is supplied from the positive supply rail, independently of the collector of the transistor. In other words, it's a three-terminal circuit; one terminal connects to 0V (the LED and the emitter resistor), one terminal supplies base bias, and the third terminal (the collector) cannot be connected to the base bias terminal. Compare it to your circuit, which has only two terminals. That is not a constant current source.
I think this is what Adam was trying to explain in post #10.
In answer to your question though, a current source doesn't have an equivalent resistance. It can be described as having an AC or incremental resistance, but not a DC resistance.
I guess what you want to know is how to set the transistor's collector voltage, to keep it at the optimum voltage of about half-way between the supply rails. You can't do that with fixed bias, because a current source doesn't behave like a collector load resistor - that's the whole point of your experiment! Using a current source as the collector load, if you over-bias the transistor, it will pull its collector way down towards 0V, and if you under-bias it, the current source will pull the collector voltage way up towards the positive supply.
You need some kind of voltage feedback mechanism to set the transistor bias to a "Goldilocks current" - "not too hot, not too cold, but just right"
I don't have time to go into detail now. Tell us more about what you're trying to do.