My theory:
The Handmaid's will dump June at the Lawrence House and will scatter back to their houses, where they can appear looking innocent at breakfast. There are no kids in their houses, so their Commanders won't even realise what's gone down till the phone starts hopping. They definitely have a chance if they get back before their Commanders and Wives get up. Maybe even after, as it seems to me Handmaid's are largely ignored most of the time, spending most of their lives in the attic. And their Martha's won't say anything. As Alma said "she's a bitch but I trust her".
So since no Handmaid's are missing, they might not be the object of suspicion.
However there will be Martha's missing. So automatically condequences sweep down on them. Im a bit worried about the two Martha's in the Lawrence House, how will they escape the ensuing scrutiny?
June will have to say she was shot by Rita. That Rita came by the house to beg for her help or something, and when June refused, she was shot and spent all night in the garden before being discovered at dawn.
If June is pregnant (and I'd bet money on it as it gives her plot armour) then she'll be a Loyal Pregnant True Servant of Gilead.
Lawrence could really take advantage of it all. Blame it all on the Waterfords (coincidence that their Martha was the supposed Ringleader? Maybe not) and even pin it on the absent Winslow.
We know at least one Commander was killed overnight. And Waterford is gone. Given that Fred said there were only 12 in each district, they are down to 10 at the most. Ample opportunity for a well respected recently widowed man who needs to hide in plain sight. He could actually become more powerful as a result of this.