At first I thought that seemed pretty unlikely as well, but maybe it's not so crazy. We know that before Kaladin ever said even the First Ideal, Syl was hanging around him and he was unconsciously drawing in stormlight and using surgebinding. He quite obviously drew in stormlight both during and after being out in the highstorm in order to survive, and he also was able to slightly deflect oncoming arrows during bridge runs. In times of great desperation or need, he's able to access these powers without knowing it.
We also know that Dalinar is clearly connected to the Stormfather, as he's been sending him visions for some time. Is his connection with the Stormfather the same as Kal's with Syl? Almost certainly not, but clearly there is some connection there. Perhaps it's enough that Dalinar could similarly draw in stormlight at a time of great need to save Elhokar.
The only thing to me that really goes against this is that we see him handling Oathbringer quite a bit afterwards. You would think that if he had any sort of bond that would allow him to draw in stormlight, that he wouldn't be able to handle the shardblade. In the end I agree with TJ, it was probably just meant to show how awesome Dalinar is as a warrior, and then contrast that to how he's trying NOT to use force when dealing with the other highprinces.
