It depends on what diesel it is, and what filtering system, and also what injection pump it has.
Fry oil has moisture in it from the cooking process. The best way is to make bio-diesel out of it, and then you can run it in all common diesels.
Running it filtered only, will probably be hard on the injection pump, depending on what pump it is...
Older diesels, like a non puterized tractor will run on filtered oil (even used oil) and get along pretty good on it. I like to mix everything like that 50-50 with diesel fuel, FILTER IT GOOD, and run it.
A couple problems with all of this is, fry oil gets very thick in the winter, and unless you heat the tank, your diesel will probably stop running. I don't run any "mix" in my diesels in the winter, it's only a warm weather deal for me.
I know some folks just filter the fry oil and run it, but most of them are shortening there injuction pump life and will pay later for doing it...
DM