Alias expansion only looks at the first token / word of a line, so there's no way for git pull !!! to get replaced by alias expansion.

However, redirects work even if placed before the command, so you can do it with an alias:

alias quiet='>/dev/null '

Leaving whitespace at the end of the alias expansion makes bash consider the next token for alias expansion. (This is why it's common to do alias sudo='sudo '). So this won't even break your aliases. Example:

$ ll *.s xyz

ls: cannot access 'xyz': No such file or directory

-rw-r--r-- 1 peter peter 12 Mar  6 20:15 a64.s

-rw-r--r-- 1 peter peter 72 Mar  6 21:03 arm.s

-rw-r--r-- 1 peter peter 30 Mar 15 17:38 foo.s

-rw-r--r-- 1 peter peter 42 Mar  6 13:12 mips.s

$ quiet ll *.s xyz     # ll alias expanded successfully, stdout discarded

ls: cannot access 'xyz': No such file or directory

$                      # stderr is not redirected.