Short answer is yes but not severely just drink a lot of water and get some minerals. You won't be dehydrated like a day under the hot sun but an awful headache can come without refueling.
I seldom cried for a good portion of my life up until a couple years ago. I now average 1-2 hours per day, every single day. Even out in public shopping sometimes I cannot even stop it. Nobody cares by the way, they avoid you just like they do the homeless.
So I started to wonder the same thing about sheer volume of crying and loss of electrolytes and fluids. I have not researched it, but consuming plenty of fluids and getting enough salt and such has helped stave off throbbing miserable headaches that may otherwise occur. Drinking the fluids also may help you feel slightly better, like 0.5-1% better or so, probably just from feeling like you are doing something positive.