Hard to say what will happen -- it depends on which microorganisms are in that honey. You may get yeast that can't tolerate much alcohol, and the yeast will be nutrient-starved in any case (honey doesn't have the nutrients that yeast needs to be really happy -- grapes and other fruits often do, but honey does not) so the fermentation may end when there's still a decent amount of residual sugar that doesn't get converted to alcohol. Maybe the final sugar content will be pleasing to taste, or maybe not.
The stressed yeast may produce off-flavors too; and you may end up with active bacterial populations in there that do things other than convert sugar to alcohol like yeast does, which can produce other flavors (maybe flavors you like, maybe not). Hence the end result may need to be aged for a long time to soften out some of the rough edges, depending on what kind of micro-menagerie you have.
So it's kind of a crap shoot. The mead will probably ferment more slowly than a batch made with commercial yeast, and it will probably not ferment to completion, but beyond that, it's luck of the draw -- if you did this three times, you might get three totally different results. You can see why people who make a lot of mead don't do it this way
That said -- it's only half a gallon, so if you're curious and you don't have unrealistic expectations, there's no reason not to try it. I have a half-gallon batch of wild-fermented hard apple cider bubbling away in my basement right now, and I think it's going to turn out well -- but again, that apple juice has more yeast nutrients in it than your honey does, and the starting sugar content of my juice was lower than your honey-water will be.
Honestly, I myself wouldn't try the experiment that you're proposing (for me, it's enough of a challenge to make good traditional mead using commercial yeast!) but I'd be interested to hear how it turns out if you do decide to do it.