You could do that but its probably not a good idea. The cigarette lighter circuit is limited to 10 amps and inverters tend to draw a lot of current. If you're only running a small inverter with a PS2 off it it should be OK but then other devices plugged into the cigarette lighter as well could blow the fuse due to over-current when the loads are combined.
To do the job properly I would run a seperate (fused!) cable directly to the battery to give the inverter its own circuit, but connecting it to the cigarette lighter circuit should be OK as long as you are aware of the possibility of overloading it and blowing the fuse if combined with using the actual cigarette lighter at the same time as the inverter for example.