Dear Brendan, 

I think it all depends on what you mean by dating. If you mean "getting into a serious relationship", then I would not only not recommend it to a high-schooler thinking of the priesthood, but to any high-schooler. It is too soon, and in most cases it becomes more that one can handle. 

Some kids call normal friendships dating, well I think normal friendships are OK and good, but they are not dating; you just have several friends among them girls and you do things together, maybe even there is one you like more than the others. 

If you mean by dating zeroing in on a particular person and giving her most of your attention, trying to spend time with her, etc then I think you have to ask yourself what is going to happen. Our hearts are very vulnerable. You can very easily create false expectations for you and her, and it can easily lead to the "serious relationship". 

Remember too, that if God is calling you to be a priest he needs you to be human, so he won't change your nature. And that means that you will always have in your nature as regards girls, initially an interest and curiosity, which can become friendship, which discovers complementarity, which encourages desire, our heart makes itself felt, and our instincts as well... Which all means that if you discover you are called to the priesthood you are going to have to learn to relate to girls in a different way, exercise some caution and restraint. 

God bless.