The answer is sort of yes, but there's a lot more to it than that as there's not enough allowance for wood movement. In short, the breadboard ends can't stretch or compress and they'd really need to in order for this to work properly.
Hidden within normal/conventional breadboard ends (when done correctly) is extra room to allow the main field of the top to expand and contract as needed — as you can see from the link above, seasonal variations in humidity result in changes to the wood's moisture content, leading to changes in width. The wetter the wood the wider the top, the drier the wood the narrower the top.
You can minimise this seasonal variation in certain ways, by selecting boards with quarter-sawn or rift-sawn grain* and by working in woods that move less than others. But unfortunately 2x material is not generally wood that moves relatively little.
So I think you need to ditch the idea of the breadboard ends.
What to do instead
Essentially all you're looking to do here is hold the two outermost boards down so they can't fall off or be lifted out of place when the table is in use, and there are other ways of doing this, all simpler in fact. And even better news, the simplest involves no extra work.
All you need to do is fix four flat expansion plates, or figure-eight fasteners, to the underside of two of the 2x4s which are then screwed to the outside two boards. This will securely hold them down while allowing them to move in or out as needed.
*This doesn't mean only how the wood was cut, it can just mean that the grain (seen from the ends) is vertical or nearly so. To put it another way, you orient the tangential grain vertically.