OP here -- to answer the question, my Honda 2000 starts on the first pull, every time. But this is the first time I have drained the carb, so I am going to do an experiment tomorrow morning, per Niner's suggestion, priming before trying to start it. (It has been so hot that I could not even stand being in my garage for the last three days -- I live fairly near the beach in Orange County, and it was over 100 degrees for five hours today. And 100 degrees for much of Tuesday and Wednesday, too. We went surfing, instead of prepping for our next camping trip. So the experiment will have to wait for the morning.)
One thing is for sure, though -- based on what I have heard here, there is no reason to leave the drain screw open after draining the carb.
