Just wondering what happens if you send your Breez wallet more than 0.04 BTC, as it says to send "up to" that amount.
After re-reading wiki which updated on late 2020[1], looks like it'll trigger refund if the channel utilize Submarine Swaps. Nevertheless, i agree with @LoyceV that you shouldn't try to find out.
I haven't used Breez, but I've used Phoenix Wallet. In Phoenix, opening the channel is custodial, but after that the channel itself is non-custodial. If you're funding Breez by sending Bitcoin to an on-chain address, I assume the same applies.
Re-reading at the wiki[2-4], looks like it's true.