Feeding a pet string made in such a way directly into an extruder would be super. It just won't happen tho, such filament is too soft and you won't be able to rigidly push it donwards into the nozzle.
I've seen experiments, to which I cannot provide the link alas, where the author folded a larger string in two along its axis, to make it thicker and stronger, and pushed it by hand through a heated extruder. It did extrude, but was hardly manageable, plus you need to device a motorized feeding method.
Producing proper filament with a DIY method is also totally an ungrateful project, here's my results: [
www.ephestione.it]