They already think this is some big scheme to kill them all. Having the nice guy die would only make it seem worse for them, like it was all part of one long con.
In which case the Watch is fucked and the whole scheme is just more ineptitude from the idiot characters in this show.
bad writing is boring, and this season has been anything but boring(save for dorne). Have fun pedantically trying to understand how stanis couldn't hear the boltons charging or how melisandre and Davos made it to the wall so quickly.
This season was mostly boring. Shock scenes are not exciting when they're done to the point of parody. Those aren't pedantic, those are genuine problems born out of bad writing. This show isn't invulnerable to it. Covering your ears and going NANANANANA doesn't change that.
Well, they still have a giant ice wall to hide behind and use to their advantage, so, yes. Easily.
Oh that same giant ice wall the Wildlings were able to infiltrate once already and the Watch have half the numbers they did at that time... okay.