Can you use a quoted string as a subroutine name?

Yes.

sub foo {say "Hello"}
"foo"->();
__END__
Hello
[download]

The reason you cannot use a quoted string, or a general expression, is the limited amount of tokes that can follow an arrow. Based on token on the right hand side of an arrow, it's decided at compile time what kind of dereference it is. Think about it, if it where delayed till run time,

$arrayref->[1];
[download]

the arrow would be a binary operator with two array references on either side.

Note that this works:

sub Foo::foo {say "Hello"};
bless [], "Foo"->${\"foo"};
__END__
Hello
[download]