Locking tuners don't (Planet Waves aside...), but the heavy-as-balls Warmoth 'Pro' construction sure can unbalance a light Strat/Soloist body. It's not going to dive to the floor like an SG or some hollows do, but there will be more weight in the neck than there is in the body and that means there's more weight bearing down on your fretting hand. Not a problem if you're sat down or use a shorter strap; quite a big problem if you like to sling your guitar lower.
That said, it's not like Warmoth give you much choice in the way of construction methods (offer Vintage Modern with tiltback headstocks already, damnit), so balance is something of a moot point. The neck is going to be heavier than the body no matter what you do, with the possible exception of having a body made out of solid maple, walnut or rosewood.
A bigger point to be made here is that with 'Pro' construction, you're getting a thicker chunk of wood for the fretboard, more metal in the middle of the neck and les swood used for the actual neck stock. So there's not so much reason to worry about the neck wood. For example, I have two Warmoth 'Pro' Tele necks, one is ebony/maple and the other is ebony/purpleheart. In theory, the purpleheart neck should be warmer than the ever-bright maple, but using them on the exact same guitar body, the tone is identical. Conversely, I've got a Musikraft neck (basically standard/Warmoth's 'vintage modern' construction) which is ebony/mahogany, and sure enough, that's a helluva lot warmer in tone, again, on the same body. That's without even taking into account metal levels of gain.
So as far as wood goes, I'd go for feel and look, rather than tone. Wenge will do you well if you want a dark look and don't change your thumb positioning much during playing. Personally, I do change from thumb-over to thumb-parallel to thumb-not-even-on-the-neck a lot, so I find Wenge to be rather grating, but I can appreciate why some people like the feel. I myself would recommend Bloodwood, Pau Ferro, Purpleheart or Goncalo Alves; you may even be able to get a neck stock made of Ebony. All of those will give you a universally slick feel with a variety of looks. Flame or birdseye maple with a tinted oil finish will give similar-feeling results with a flashier look.