1. In principle, yes. That is if you put bio-diesel in the tank it would run. Turbines will run on a variety of fuels.
2. However, it isn't approved. so it wouldn't be legal (I imagine). In my experience, AFMs almost always limit use to certain fuels.
3. It would also be sensible for some bench testing (i.e. on the ground to be done). I am sure this would be needed in order to get 2.
4. I also wonder whether you might get problems with water in the fuel, like you do if you use ordinary motor fuel (MOGAS) in a piston engine. When you go to altitude (i.e. cold) the water freezes and can cause all sorts of problems.
Quality control of your alternative fuel has to be a priority for flight safety, if you value your life.