You can also turn the cage on it’s side and set a feeding jar on the screen so the girls can get to it don’t be afraid to install them if the weather is not perfect. I have install bees on days that were cloudy and in the mid forties. And have not lost a package yet. The sooner you can get them into a hive the better as long as they can cluster they will keep warm
Probably not a bad idea IF the feeder can is empty. If it's not empty it may cause the syrup to run out all over the bees. I lost several packages when the post office layed them on their sides and the syrup all ran out on the bees.