If you pulled the cork from the candy end or in case of california mini cages put a marshmallow or candy in the cork end and insterted into the hive it will only take about 3 days max for the girls to release the queen. If you leave the cage in longer they may try to start building comb around it. I go 3 days after insertion of a package, remove queen cage,(as long as she has been let out), straighten up the frames and then put hive back together and leave alone for 9 or 10 days. This gives you time to allow the queen to get to laying good and when you inspect in 10 days you should find all stages of brood including capped. This time also gives you peace of mind that if you happen to roll the queen or hurt her while inspecting the girls can supersede with no problems using eggs from her. As for the taking of the syrup, some take it heavily some don't. All depends on situation and if they have more nurse bees or not, as well as any drawn comb or not to start off with. I have hives that will pull down a half a gallon a day and others that will pull down the same in two days. Just depends upon how fast she is laying and needing the comb area. They will only use what they need and if they find other sources outside that is natural they won't touch it.