As far as I know, there's no party on earth who could execute a space mission on one month notice. And such a mission would have very little capabilities due to poor preparation time.
Whatever doomsday scenario you are concerned about, it's not a realistic goal.
And an impending catastrophe so urgent that it needed an immediate launch would be unlikely to leave Russia or China unaffected, so any breakdown in relations would be quickly put aside for the sake of [deflecting meteors/fighting alien invaders/saving the moon from being eaten by a giant space shark].
No, I very much doubt that. If there was a launch vehicle and space craft ready and waiting for integration, it would take about a month to get it on the pad and launched.
But there aren't any spare rockets lying around like that. And we're talking about a standard LEO mission, not a doomsday scenario one off special mission.