I have used foliar application on honeysuckle in the following manner. On a fire break in a ruderal area with no native plants I had mowed down all sorts and sizes of honeysuckle and other woody plants. The fire break was about 30 foot wide and maybe a quarter mile long. I made a solution of 4 ounces of Progeny per gallon with 2% methylated seed oil. I applied this mix with a boomless 50 gallon Kings sprayer from a 30 horsepower tractor. After two months the application had a good kill on the smaller sized honeysuckle and other woody plants, and had set back the bigger plants, but maybe it was not going to kill them. I expect I should repeat that next year for better effect. If I tried to do that job with a backpack sprayer it would have taken me days.
Another time to foliar spray honeysuckle could be when the plant is really short, like when they re-sprout after fire or mowing. Let the plants emerge several inches and turn green. I applied our 17% Garlon 4 basal bark mix to the leaves and stems of about 40 plants. I painted a bit of blue on each one. All were dead after three months. I bet I could have sprayed them with Progeny or glyphosate and also gotten good results.
So my bottom line is you can use foliar spray in ruderal areas or spot spray on short emerging honeysuckle. Foliar spraying tall shrubs in good vegetation will yield a big circle of off-target kill.
I have two more posts on honeysuckle, one on mowing and one on pulling it.