Many X-mas lights will have problems like described, i.e. allowing leakage current, or applying voltage to thing like shrubs with, or without a GFCI. With a GFCI you really can not bet on it to trip if a hazard presents itself. (I would not bet my life on it! In fact I have been shocked by some before in the rain, that were on a GFI.) Water, and electricity just don't mix well. If it is a liability issue, I would say no. Don't install the lighting. If it is a convieniance for some moron to do what they will do anyway, advise, and step back. Just because they are listed, or manufactured for the purpose, is NOT a guarantee of 100% safety. Personally, I would not operate, or handle them in the rain, or when wet. Like using the blow dryer in the shower or tub, just a bad idea, GFI or not. The fact that it has a GFI is only an added protection, NOT a guarantee of being safe from a darwin award. The hedge might not be a great conductor, but a small child touching it could be. Just my 2 cents.
