On the 3.5 the engine will run off of residual pressure and fuel vapor through the fuel return network. It will die as soon as you put it in gear, but it will run.
the big issue on the 3.5 hot start seems to be with fuel volume delivery from the pump. the engine will run decently on 1 liter of fuel a minute, but when it gets hot, the fuel rail fills with vapor, and often an old pump can't deliver enough fuel to overcome the vapor lock for the car to actually start and run decently. I am wrangling with this issue on another 3-5. it seems the replacement pump I got can't take the heat.
fuel volume delivery, hot, should be a litre in 30 seconds.

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Pierre Hedary 1985 280SEL, 1970 111.026 in progress
Mercedes technical advice hotline: 407 765 2867
[servicing older Mercedes in the state of Florida with competence and passion].

From the standpoint of an honest MB technician, Vegetable oil is a threat to your diesel engine's mechanical integrity.