Turbine helis burn Jet-A. Anything that'll burn that will likely burn biodiesel.
"Some people I know" once burnt tankfuls of diesel in an early morning multi-helicopter flight some years back, due to an unfortunate combination of circumstances leading to the glugging of said fuel into the tanks rather than avtur.
The only bad outcome of that was that once the stuff-up was discovered, a whole lot of defuelling, filter changes, pushing around of heavy helicopters and ground running (plus the red faces of course).
Biodiesel would no doubt have worked fine too; good to know that a turbine engine probably won't stop dead anyway (at least in the short term) if you put the wrong stuff in.