That depends on how the alarm is designed to handle the sensor being connected or disconnected. If the alarm has no configuration to say "there is a sensor attached on this particular input" and does not go into fault when there is no sensor present, then it will be fine. If the alarm has a config to say there is a sensor, and WILL go into fault when it's not connected (which is a security measure that proper designers would think of) then it might not work.
More likely, the alarm is so shoddily designed (with respect to circuit integrity and security) that simply plugging the sensor in is all that it takes to "enable" the input and disconnecting it is all that is required to disable it. Cutting wires is equivalent to disconnection. In this case, it won't even notice.