Case and point: Do you pay for PkHeX? No? Sit down, be quite and wait
"I'm unsure if they connect online to verify the transfer process, but given that I bring my CFW Switch online, I've never really checked (my internet settings are saved on that Switch)" You better believe it does lol! I had a CFW switch and a non-CFW switch and was doing this exact thing. 1 1/2 weeks later, i got the ban hammer from Nintendo on my CFW Switch Many updates prior, i don't believe the profiles had to connect to the Nintendo servers to verify, but now they do unfortunately...