Skipping nursing while triple feeding [BC]

My 3 wk old does not suck more than a few minutes from my breasts before falling asleep at the breast. We have had to supplement most feeds because she is usually still hungry. I also have a low supply although it has improved somewhat over the last few days of cluster feeding. We met a lactation consultant today who felt baby doesn't suck well because I have a low supply. She recommended I try triple feeding for 72hrs. I am not sure I completely agree but willing to try it. I did ask if I can skip a nursing session and directly pump and bottle feed. She said that is okay. Because I am not sure I completely trust her recommendation, I thought I would ask here if skipping a nursing session and pumping will impact the goal of improving her supply and hoping she transfers more milk. I also didn't get a chance to ask because the appointment felt so rushed but what would the point of doing this 72hrs be. Wouldn't my supply just dip once I stopped because the baby would still not suck well?