Does nursing count towards motn pump?

I see a lot of posts and convos around the motn pump and how it helps increase/maintain supply. my question is do we count a motn nursing session the same as a pumping session? My understanding is that babies are generally better than pumps at emptying our boobs and stimulating milk supply so I would think that a motn nursing session would accomplish the same as a pumping session. Is this right? Thoughts?

I have a 7 week old and right now my last pump is around 9/10pm. If my baby wakes up for a feed at around 1am, I’ll pump, but if he wakes up at around 3am, I’ll nurse first then supplement with a bottle until he’s satisfied, but I don’t pump. I’ll nurse again around 6am and my next pump isn’t until around 7am. My thinking is that nursing until boobs feel soft and “empty” is interchangeable with pumping. Do other people have a different opinion? My supply was super delayed and I’ve been trying to get it up since my baby was born so I don’t want to do things that’ll hurt my progress. I do have a lactation consultant I can discuss this with, but I’d love other opinions based on personal experiences. Thanks!