She is the MP, and she would remain as the MP even if the vote of no confidence had been passed. What this looked like it was about is who gets to be the next Labour candidate; personally as said above I would rather the CLP have asked her whether or not she actually was going to be that candidate. This is not an unreasonable request given that its them who do the door-knocking, the leaflet drops, the speaking to people in the street, and when she has been going around implying that she was considering quitting the party.
I live down in London and have nothing to do with that CLP (though mine has also had a vote of no confidence passed last year, but it was for Kate Hoey so there was no round of solidarity on Twitter or indeed any expression of support), but for Watson to call for the entire CLP to be suspended before a motion is even voted on (and imply they are all bullying their MP) is a bit much.