Can't believe I haven't thought of this! I've been using an Apple BT keyboard with my MBP but never thought to stack it right on top of the butterfly keyboard. I can confirm that it fits the 13" MPB, just like your 15"!
Update: my Apple BT keyboard (which is many years old -- it takes 3 AA batteries, not 2) slightly covers the top of the trackpad on my 13" MBP. This means that the palm rejection algorithm does not work as well. I may be able to get it to work for me by just adjusting how I hold my hands when typing, but it's not a clear home-run with my smaller laptop and possibly larger keyboard. I would seriously consider getting a smaller BT keyboard to make this work, though.
Haven't tried that, but it really sounds it would be terrible to the wrists after prolonged use (in which case "prolonged" would mean longer than 10-15 minutes).