Short answer is no, unless the seller can provide a written letter (like this one) from the subscription company (ie ADT, etc) saying that all sensors where needed (in all bedroom, bedroom hallways, etc) will sound an audible alarm loud enough to wake sleeping occupants in case of a fire or smoke event event if there is no paid subscription in place (as the buyer may choose not to subscribe to this service).
Short of this requirement, the seller should be prepared to consider their ADT or other system simply a ‘back up’ for their primary system of smoke and carbon monoxide detectors. This may look unsightly as now there are two detectors where there could only be one.
ADT and similar systems can not be tested reliably by anyone other than ADT or whoever the system is with, as all security systems are different. Triggering a sensor to sound may also trigger a call to the police or fire department. All systems are different and proprietary. These systems also usually run off a low voltage system versus a normal 120 volt AC system like normal detectors.
Bottom line – get a letter from ADT (or whatever company it may be) stating what services will work if the new buyer does or does not subscribe (or pay for) a new service contract. Will the sensors sense smoke? carbon monoxide? fire? A bunch of questions here. Both seller and buyer want to be clear and not make any assumptions as to what this type of proprietary system may or may not do upon purchase of the home.
Here is an example of the letter that should be received by the security system in question.