check which channel you're signed in as before you hit delete. if you've got more than one (brand account ones especially) the settings page acts on whichever is active, and people have deleted the wrong one.
it doesn't touch your google account or gmail either way, just the channel.
the app doesn't carry the option at all, which is where most people come unstuck. do it in a browser.
youtube settings, advanced settings down at the bottom, delete channel is in there and it makes you sign in again to confirm. next to it is a hide option, which pulls everything out of sight but is reversible. i'd take that one if there's any doubt, because deleting takes your comments and subscribers with it and there's no undo.