Generally, biodiesel will not climb a wick. That said, however, ir seems that once the wick is saturated it does stay lit, but the flame is not strong and can easily be blown out. A mix of biodiesel and kerosene will do a much better job.
We have been able to get B100 to burn in a Tiki lamp, but it doesn't take much to blow it out, but once K1 is added it fares better.

HTH