No, only the attributes listed in the documentation you reference are supported. E.g. "locked" is supported but "Constructor" isn't.

Correction: "Arbitrary" attributes need a handling subroutine (of the same name as the attribute) to be defined in your class. That facility also needs to be turned on using Attribute::Handlers. Your code will then only work on v5.6.0 of Perl onwards and so should therefore formally require that version (or a later one if otherwise appropriate). For example:

require v5.6.0;
use Attribute::Handlers;
package Whatever;
#...
sub Mutator : ATTR{CODE} {
    my ( $package, $symbol, $referent, $attr, $data ) = @_;
    # ... do whatever you want with mutators
}
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User-defined attributes can apply to other types, not just CODE as also explained in the documentation.