Does the NK actually have capability for that? Without nukes that is.
Just going to note that will and intent do not really matter for military strategy and planning, only capability matters and must be taken into account.
No they don't. The thing about shelling and bombing is that once the first couple hit, people scramble for cover, and the more buildings you wreck the more cover you create and the harder it becomes to inflict further casualties. Seoul is a positively huge city. It would cause a lot of deaths and injuries, but it wouldn't come remotely close to wiping out all the inhabitants of Seoul, it probably wouldn't come close to wiping out a tenth of the population even if the barrages were allowed to continue unabated (note that this is still a huge number of people, I'm just trying to give a sense of scale). In reality, they won't get a whole day of pounding even with access to unlimited shells (which they definitely don't have), because the ROK armed forces will be doing their best to hit as many artillery sites as possible and will be employing counter-barrages when the North Korean assets open fire. If you imagine a preemptive strike, it becomes even more difficult for the North Koreans as they would only have a fraction of their assets online in the front line ready to go, and civilians will have been warned before the firing starts.
From the SK perspective, attacks on Seoul are their worst nightmare. But from a North Korean perspective, shelling Seoul en masse is an implicit concession of defeat, since the civilian population of the city has no military value; it means they'd wasted massive quantities of munitions on this one punitive action instead of targeting the military assets that are about to return fire on them with far more sophisticated and accurate weapons systems.
The damage that NK could do with strategic weapons is far higher than the damage they could do with conventional weapons. One low-yield nuclear weapon will be far deadlier than conventional artillery barrages on Seoul will because it's effects are near-instantaneous. I would be far more worried about that. Even with patriot systems installed, I'd be concerned that I couldn't tell the difference between short range nuclear weapons and more conventional rocket artillery systems. The North Koreans have plenty of SCUD-B derivatives, more than could ever be intercepted with current systems.