Tested heavily and no dice. Mobile off or not online my payments to that account would not go through, perhaps I have missed something but that was my experience a month ago and with two different mobiles.
I saw you guys just made a theme update that looks amazing plus some changes that should improve the wallet functionality, will test it again, really liked what you guys are building and you are clearly working hard on that wallet, additionally, you are very responsive and present here in Nostr, that is very much appreciated, you guys rock!
Get the yesterday's over the air update. There was a bugfix for a recent regression bug that prevented to claim sats coming to lightning address unless wallet restarted. It is now fixed and wallet tries to claim on start, on coming to foreground and then every 60 seconds when actively in use.