Keyfobs are ran off RF frequency, at specific tuning point. If the Mazda's are the same as the VWs (say 799mHz) it may be possible the the fob be programmed for the car.
The other side of me says absolutely not. Alarm companies specifically use different frequencies so theifs have to keep guessing. Most aftermarket alarms use Rolling Codes, meaning they change "identification numbers" every time the button is pressed.
Now the factory may not use the Rolling Codes method, but I think the likelyness of it working is naada. Some factory keyless/alarms are made by Code Alarm.
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