No experience on a single battery and inverter, but. It depends on the amp hr. rating and condition of the battery. A middle of the road great shape 660 amp hr. battery will only last appx 4.75 hrs @ 1000 watts.
900watts at 12 V = approx. 80 amps current draw. That is probably 7 times the drain of leaving your lights on. Every time you deep discharge a starting duty battery really reduces its life expectancy so keeping the engine running lets the alternator take the load instead of putting it on the battery debit card which costs you interest.
Check with JC Whitney. You can but a battery isolator (sp?) and an extra battery tray. Get a deep cycle battery and hook it up on the other side. The isolator will allow you to drain the aux. battery without discharging the starting battery. Absent this, yes-run your truck.