If a hive have comb all ready drawn,do they collect more honey ?
Not more but it sure is faster. I use already drawn comb when ever i have some, the queen has somewere to lay non stop, no waiting for the frames to be drawn, then if they have room they can store right away as well. if you use a honey super full of drawn frames, sure it is filled straight away with out them drawing it first. so its seems faster, but collecting more?? naw they collect the same amount it just they have a place to store it faster.
I would have to say yes, there would be more honey. Look at what it takes to make all that wax. When workers are roughly 10 days old, they develop special wax-producing glands in their abdomens. They eat lots of honey. The glands convert the sugar in the honey into wax, which seeps through small pores in the bee's body leaving tiny white flakes on its abdomen. This is where the wax comes from, converting a lot of honey into wax. If they do not have to make as much wax, they do not have to eat as much, saving the honey stores for you to rob.
I would say possibly so, particularly if there is a weak flow on. In a weak flow before they can fill and cure nectar in cells they need to draw out those cells and that does require time and effort on their part. In my opinion placing already drawn comb in a hive during a weak flow just may allow you to pull honey you otherwise could not.
In a strong flow, you are still minimizing their work load, so either way, my answer to your question is yes.
...JP