No, uncorrect. All evidence points to iOS needing anyway to mix the music with the system sounds (think notifications, ringtones, etc.). To do that, it must decode the AAC files coming from Apple Music and then, after mixing, re-encoding them in AAC to send to the headphones. If this second process happened with LDAC, you'd theoretically gain in quality, as LDAC has so much more bandwidth available. LDAC streams at 990kbps (when prioritizing quality, I do that and I've yet to experience a drop in connection during normal use, with a Nexus 6P), while iOS streams AAC at 256kbps.
While true that AAC at 256kbps is perceptually transparent for the grand, grand majority of users, in your case you'd be transcoding from a lossy format. Music was already compressed when coming from Apple Music, you decode it and then re-encode it. In that case, with LDAC, you have so much more bandwidth that, theoretically at least, you might be gaining something in quality.
Personally I think that, given that you are transcoding only once, you are fine with your phone. Online you can find tests that expose the limits of multiple transcoding, after many passes it gets really bad. But not after one pass, I think.
