Will the admission committee actually read a student's paper mentioned in resume?
While it's a single N experience from my graduate school application process:


  Does the admission committee even bother to go through the paper to
  assess the work quality? (Sometimes, you can have a rough quality
  assessment by looking at which journal/conference the paper is
  accepted by)


Yes. Several interviews I had mentioned content within the paper, at at least one of them had a good 10 or 15 minute discussion about the research that didn't start with the phrase "So, tell me what your paper was about..."


  If the answer is positive, is it a good idea for the applicant to
  upload the papers to arXiv and provide the committee with the links so
  that the committee can read the papers as they wish?


Yes. If your field is arXiv friendly, put it there. If your field isn't particularly arXiv friendly (like mine) and your paper is in press, consider providing the PDF as a supplement to your admissions packet.