I try to thing of beveling as just REALLY low angle sharpening, like at 2.5 degrees per side or something. If you think of it like that, then yes, the tip should be at the same thickness as the rest of the edge. However, its a little more complicated than that. With sharpening, you know you're going all the way to a sharp edge. With beveling, you know you're (usually) going to leave a flat at the apex of what is a very skinny triangle, using a flat ground blade as an example. All the angles can be the same, the only question is how wide is that flat spot on the edge. I'd say at least 90% of knives are made with varying thickness of that flat spot, just for the reasons discussed above. Someone sent me measurements of a Busse's edge thickness, just at the top of the sharpened edge. It varied from 1/32" at the handle/choil all the way up to nearly 3/32" at the tip. However, the edge angle was the same from the choil to the tip, a very even 21 degrees, by his measurements. Now Busse's are meant for hard use, and so this seems perfectly reasonable. However, I would be very disappointed if this type of thing happened on the clip blade of my trapper slip joint, and it doesn't.
That may be the place to look, if you are so inclined. The various old style slip joints have much better cutting geometry than modern tactical folders, even putting the much vaunted full flat ground Spyderco models to shame. My dad's old Parker Cutlery trapper still had an edge that was only 0.01" thick at the top of the 12 degree edge bevel, and he had it so long there is a visible pocket worn line on the blades that stops at the point the blades go into the handles.