If you heated it per instructions and used wood chips per instructions, then no, you don't need to do it again, water or not.
When I went to do the pre seasoning of my master built electric smoker. I put water in the pan and went through the whole process. Should I go back through the process again, with no water in the pan?
You sound like me, concerned that I made a major mistake with something. I agree with the advice here but I think you really want to pre season it again without the water. If it gives you peace of mind go ahead and do it if you haven't already. In the long run how you pre-seasoned the smoker won't mean a thing.
When I went to do the pre seasoning of my master built electric smoker. I put water in the pan and went through the whole process. Should I go back through the process again, with no water in the pan?
You just remarked on something I've commented about for a while. If you look at pro smokers either in restaurants, competitions, on TV, the insides of all of them are black with all the stuff you described. I understand newbies wanting to keep their smokers liking as new as the day they opened the carton but--c'mon, guys! A smoker was meant to be used and to look used. I look with the same askance at people who strive to scrub their stainless steel cookware spotlessly clean! Look in any restaurant kitchen--you won't see spotless cookware unless they're brand new. And they won't look like that for long.
Unfortunately. the Seasoning of a smoker, that which gives the magical extra flavor, does not come with a couple hours of pre-seasoning smoke in a new smoker. It takes many many hours of smoke and buildup over weeks or months. Look at the top restaurants in Texas, KC and Carolina's. Fifty year old pits with inches of burnt on grease and smoke. I have 2 MES40's, mine in NJ is one season old and my Daughter has the 4 year old smoker in PA. Her meat just taste better, my recipes, my timing, but a well seasoned pit.
If it makes you feel better, light it up and let the smoke flow. If you are Hungry, throw some meat in and let the magic begin...JJ