I know \"Ayy can append current line to register a.
How do I append current line to unnamed register?
You can use this
:let @"=@".getline('.')
to append to the unnamed register. I do not believe there is a keyboard shortcut to do this. (However you could create a mapping if you wanted.)
The reason I say that there is no keyboard shortcut for this is because :h quote_alpha only talks about uppercase letters (for appending). And there is no equivalent statement in :h quote_quote