The Ecolink (and several other similar product) include terminals on the inside that you could connect directly to a magnetic reed switch.
With a little ingenuity, you should be able to to have the reed switch send a signal to both the alarm system and the zwave /zigbee sensor.
Of course, for the cost of doing this, you might as well just replace the whole thing with a wireless system.
Ecolink Intelligent Technology Z-Wave Easy Install, Battery Operated, Door/Window Sensor, White & Brown (DWZWAVE2-ECO) https://www.amazon.com/dp/B00HPIYJWU/ref=cm_sw_r_cp_apa_MROzBbB70E484