For successfully using your notation, the import() routine of the imported module must be aware about and know what to do with the additionally supplied hashref, so, no per default.
My question is, what for? If the function is to be called once after importing, use a BEGIN block after the use MyModule to do so. If MyModule is your module, modify the import() routine so as to call the function immediately with the parameter passed in the hashref, if it's present.
But if you want to set a default parameter for that imported function for every call, you could say:
use MyModule qw(MyFunction);
BEGIN {
my $subref = \&MyFunction; # already imported
*{__PACKAGE__.'::MyFunction'} = sub { $subref->('HelloWord', @_) }
+;
}