Yes if you notice it in the videos you absolutely will notice it in-game. It's just everywhere, the only thing in focus is your dashboard or car depending on camera view.
I'm stunned they released it like this when so much care and attention has been lavished on every other area I've looked at.
I've been driving some of the older cars, a couple I've actually driven the real thing of, one I've even owned, and that's been a blast. I can confirm that old Fords with souped up engines are exactly as dangerous as the game depicts.
If the devs are still reading this, please let us turn the blur off completely. I saw a slider mentioned so as long as the bottom setting is 'none' we're all good to go. If that causes a loss of AA then fine, I don't care - just give us the option to fix the blur please. Oh another suggestion - in menus let us move upwards from the top to wrap around to the bottom. Small thing, nice to have though.
According to the devs, it's an image quality enhancement. For example, your car from behind view, when you are not turning, looks very smooth on the edges, even better than PC. When you stop completely, everything looks butter smooth. The whole image breaks going above 5km/h sure, but if you go above 50km/h, all the road-side objects double, giving a massive boost of objects visible on screen. PS4 version boasts double the amount of fence rods, road cones, lamp posts compared to other platforms.
On a serious note, if they allow turning off the temporal anti-alias, please provide a similar motion blur setting that produces actual motion blur on anything other than road pebbles. Xbox One's motion blur seems perfectly fine, it's not overdone, you can still view slow moving objects in detail (as opposed to everything that moves two pixels across frames having a ghost on PS4). The motion blur on XBox One provides sense of speed that the ghosting can't, for reasons I'm not going to cover here.