From Dalinars trips to what ever it is, I think it's been inclined that all of the Radiants seem to have some form of Surge power.
As you've already pointed out, Dalinar is offered to go and train to become... something. Does this mean that the Surgebinding can be taught?
I doubt that it can be taught because then it would've most likely been passed on to others through the 4000 years and would've been some what of a normality. As it seems now, it's very, very rare.
So to sum this post up. No bridge four wont be the new batch of knights. However I believe more and more people will discover their new powers through out the course of the books.
However. If it were to be that bridge four became the knights. I'd love if they established the name Bridge Four instead of the wussy "Knights Radiant".