The actual quality of the speaker doesn't matter so much as long as it reproduces the right frequencies with enough oomph (if you have quite a deep voiced speaker on a tiny phone, you can end up with it being all mushy and requiring more attention). The immersion really comes from the human speaker which can vary dramatically and ideally I like to have the author. I used to listen to audiobooks whilst walking to the pub (man I used to spend a lot of time at that pub) but when I got there and sat in the corner with my pint like the old man I pretend to be, I switched to reading Private Eye magazine. As you can tell, I therefore use audiobooks whilst I'm doing something else and so there's not really the opportunity for immersion. There is something that I think is called immersive reading where you hae both the audio and the text at the same time. I've never tried this and I think it's limited to certain e-readers.
I agree that OLED screens are damned good for reading on compared to most LCDs but if you get a high res quantum dot LCD screen it seems to be pretty good also. I have this on my Kindle HDX which is showing its age but is still damned fine.
I have tried listening to audio books in a dark room to try and get the same immersion and concentration you get from a really decent book, but... I fall asleep. This is likely a result of the quantity of painkilling medications I take and so your mileage may vary.
What I'd do is give it a go - find something cheap on Amazon (or if you're cheap like me, download the audio track of one posted on youtube and play it using VLC on your phone, ahem.) and give it a go. The ones that really stand out for me are "Lying" by Sam Harris (more because of the content than the quality of the reading) and the one I'm listening to now which is the Gulag Archipelago which was recorded decades ago and the guy reading it has clearly read it several times in order to put the passion and dark humour of the author into it.