Ought food processor blades be sharpened or replaced?
First things first, as it was very well pointed in the comments - food processor is not a 100% substitution for knives. It helps to do bulk processing of the more laborous knifework (slicing, brunoise, etc.) and also to do things that you cannot do with other tools (pureeing raw stuff)


How long do the blades last, if they food-process raw hard unpiercable vegetables like 1 winter squash daily? 


See first point above. The skin and seeds should be removed before processing. Winter squash is very pierceable with a sharp knife - I did dice a kabocha squash with only a knife yesterday. If you take good care of your processor and do not try to use it on things it is not supposed to be used, the blades last for a very very long while - it is more probable that your processor breaks instead of the blades going dull, especially if they're serrated blades.  


Can the blades be sharpened? r/cooking contends yes.


Depends on the blade. If it is a smooth blade like the older models, yes, you can resharpen them. My mom has an old-school processor that is older than me and she had the blades sharpened quite a few times. If it is a serrated blade (designed for longer durability and less dulling), you need to go to a cutler / knifemaker if you really want to keep it because the serrration is very fine and difficult to sharpen using the sandpaper method.


Even if they can, is it cheaper to sharpen or replace the blades?


Depends on #2 and your location (i.e. how much would you pay for sharpening a normal knife and how much would you pay for sharpening a serrated knife), and whether or not you can exectue proper sharpening by yourself.