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Of course, the answer is not that simple: mud is for both strength and looks. It is also for insulation, to prevent drafts through the wall.
As for strength, although it does not add a tremendous amount of strength, the mud combined with tape (in between the joints) helps turn the seperate pieces of drywall into one, solid unit that can withstand (and help prevent) a minimal amount of shifting.
The real benefit of mud, and the benefit of having a skilled professional do it, is cosmetic: it turns the seperate pieces of drywall into one smooth, sleek unit.
A sloppy mud job will mostly just be a cosmetic flaw. So long as they put tape between the joints and filled the gaps (which I cannot imagine they did not do), the wall should be strong enough and nonporous enough. They might not have pushed the mud deep enough into the joints for an ideally-strong fill, but if they did not leave long, large gaps between the joints, it should be structurally sound and should prevent drafts. It is just ugly.