When you stop your contract with them, will they leave the system in your home?
The reason I ask is because we bought a home that had a unit from another security system, and we did not want the service. As it turned out, they did not remove anything because of the work involved. The unit remained completely operable, except it did not call the main security office when set off.
Basically, your Brinks unit, if they leave it behind, should still have the ability to be armed, and would still go off if tripped. If yours is a completely silent unit, you should also be able to add an alarm bell to it.
See if they will leave the unit in, and also see if you can get a system schematic from them.