You are not going to get the inside of the smoker down to factory painted metal, so that is not a worry. The worry is that if you let the build up continue, it gets mixed with grease and can become flamable.
I asked Grandam about the cast iron and here is what she said.... Absolutely not. The soap will change the flavor and you'll never get it out.
Here is the catch, cooking on a cast iron skillet and cooking on a smoker are two different things. In the skillet, the meat comes into direct contact with the food. When you are finished with the cast iron skillet, you still wash it and reseason it before putting it away.
Even Brinkmann provides instructions for degreasing a smoker or a grill. Again we are not talking about down to bare metal. The coating helps prevent rust. What you don't want is for the flavor of old or stale smoke getting into your food.
And this is one of those things that people will have a lot of difference of opinion on. There is no set answer. I own a smoker that is over 20 years old, a Brinkmann SNP. I have cleaned it maybe 3 times. So again, i'm not promoting that anyone clean their smoker after every use.
But the answer to the OP is yes, you can clean out your smoker.