Just went through a toolbox search. You can definitely fit a chest style, which does not extend up above the truck bed rails. The only question is what size will fit.
Take a look at this link below. This particular one would fit, but more importantly, scroll down to the bottom of the page and see the list of all their chest style sizes. Other brands have similar sizes.
Weatherguard Tool ChestI think you could also use a low profile cross-bed saddle style, since you have a slider, and some of those are even narrower, as small as 16" wide and 13" deep. That shallow depth might be helpful to avoid the front hitch mounting rail or puck.
You'll be in a better position to search once you get your hitch mounted, but the short answer is you can definitely fit a toolbox.
2006 F250 Diesel
2011 Keystone Cougar 278RKSWE Fiver