I imagine this as an experiment with a VW Rabbit diesel after the doors fall off. I suspect the particulate output and general fouling with soot would be rather nasty.

The engine would certainly have to be hot. And ideally, the oil should be preheated to thin it out. Don't try it in a cold climate; even after conversion, biodiesel gels rather easily.

And would the injectors clog running fast food fat (like arteries, perhaps)?

Horsepower falloff? Perhaps. Might be more suitable for a stationary generator than a car on the highway.

In a survival situation, at least in the longer term, calories will trump fuel. Feed it to the creatures that feed you.

Last thought: used cooking oil from fast food joints is now worth a substantial amount of cash. It's not waste any more. So it's best to have a legit source (i.e., ask permission).

If anyone tries this, make sure to post the results!