What effects (if any) do audited undergraduate courses have on graduate admissions?
My question is: will this have any positive benefits while I'm applying to graduate school?


I think you are asking whether it will make your application more competitive.  Answer: not much.  At many/most universities, anyone can audit any course at any time, and it doesn't certify anything more than that they showed up for class -- in some cases not even that.  I had an auditor in a course this semester who showed up 
for the first half of the lectures and not for the second half.  My response: ok.  It shows up in my records -- so presumably also hers -- that she audited the course.  I am not asked to assign a grade of any kind.


  Or would the admissions committee assume that I didn't learn as much as someone who actually took the course, and take it with a grain of salt that I know the material?


They would probably not assume anything at all.  They would certainly not regard this as being evidence that you learned the material: getting a poor grade in a course certainly does not demonstrate learning of the material, and auditing shows less than that.  

Of course you can learn things by auditing a course.  But you can also learn by outside reading and in other ways.  However most students at this level learn more by actually taking a course, and of course if you do well in the course then that knowledge gets certified (to an extent) and can be used advantageously in your graduate application.  

Story check: you say that you have two years left of undergraduate study and can't find time to officially take one course that you think will be beneficial to your intended graduate study.  This professor who read graduate applications for several years finds that hard to believe.  In two years you should be able to work in the time to take one extra course, e.g. by (i) taking courses over the summer or (ii) getting excused from one course in a sequence, say by taking an exam which shows your competence.  This is something to talk to your undergraduate advisor about.