Nest Protect doesn't integrate with non-Nest smoke detectors. You can by all means use both, but they will operate independently of one another. If Protect sounds an alarm, it won't sound on your non-Nest detector (unless of course that detector also detects smoke or heat (depending on the detector type). This of course is one of the great features of Protect. If one Protect detects something is wrong, the alarm will sound on all your Protects.
