YES it does however, she wasn't 'missing' she was 'abducted' via a window according to Mother Kate first on the alleged 'crime scene'.
It really does help if you stick with the program. You will recall the suspporters here are arguing, from 10 years on and with nothing else to go on but Kates word, that From her initial knowledge about a door being 'ajar' to opening the door she KNEW RIGHT AWAY.
So, knowing right away.. she checked the apartment, then ran out knowing of it her daughter was 'abducted' leaving two babies,then the tapas group went to check again knowing she was abducted...
...and the toad turned into a handsome prince... Some people are better than others at making up stories.
Even if Kate did know in her heart that Madeleine had been abducted - that wouldn't stop her from hoping against hope that she was wrong.
IMO the reason Gerry checked to see if the shutters could be opened from the outside was to find out whether it was possible that Madeleine could have opened them from the inside - even though he knew in his heart that she couldn't have done that.
They were in the first throes of every parents worst nightmare - something which it appears you have no ability to understand in the slightest.
IMO