Yes, but I've read the better designs run cleaner. The bottom line, in a post-EMP (terrestrial or from the sun), a gassifier could be used. I'm thinking a central power unit for a small town that could run a generator or two to pump water or run a tractor. A small one could run a splitter, but hauling the wood would be an honest cast iron pain in the butt.
The tractor would feed you, the water pump would keep you in water. Considering the other options, I'm looking at what elevates my family in the ever remote chance something like that happened. But you are multiple steps ahead of me since I'm not much of a fabricator and haven't built one. So, I'm boned for the most part. I'm at least thinking about it, so I have that going for me.
If the EMP was so bad as to cook all vehicles etc then your grid is absolutely fried. That would include all the transformers, wiring etc. Your generated electricity isn't going to go anywhere. Most municipal water pumps are now electrically driven and if they are not they usually run on NG and are heavily electronic. Most of those aren't going to be retrofitted to mechanical very easily from local parts. As for the tractor Get an old diesel tractor and be done. All mechanical except for the starter. Keep a spare starter, solenoid etc if you are that worried. Diesel is everywhere and if it is as the book played out there would be no shortage of diesel. Splitting wood is the easiest part of wood cutting. Try felling and bucking by hand. That sucks and you need the tools to do it. One man or two man saws,axes and the skills to use and maintain them. It takes me 2 years to dry down my hardwood firewood and the fuel for a gasifier needs to be at least that dry if not drier.
I say all this not to dissuade you from trying it but try it now. Don't pull out those FEMA plans after the fact and find out you cant build it or you are missing a couple components. If you were counting on it and it isn't feasible you are now screwed.