Big, a 900 watt element and the 125 watt puck burner will consume about 8.5 amps. It has been reported that the fuse on the power supply to the smoker (located in the smoke generator) is a 10 amp fuse. The normal recommendation is to not exceed 80 percent of the rated capacity of an electrical circuit. In this case, 80 percent of the 10 amp fuse would be 8 amps. So, the 8.5 amps required by your proposed element configuration would exceed the recommended load by a little bit. So, you could probably run your proposed configuration without a PID, but it would exceed recommended load limits.
Another thing to consider is what you are smoking. Since a PID is used primarily to improve temperature control, if you are smoking products that would benefit from improved temperature control, such as sausage, fish, or cheese, you might want to invest in a PID anyway.