Is it possible to have both inappropriate sinus tachy and paroxysmal atrial tachy?

Probably yes. I'm not sure what you mean by "inappropriate" sinus tachycardia, since there's usually some underlying reason (like fever, anxiety, anemia, overactive thyroid, poor heart function, etc), but sinus tachycardia is different from and can happen at different times to the same patient with paroxysmal atrial tachy (where the heartbeat is suddenly generated by an abnormal area of the atrium ).