I don't know for certain. But the one problem with using terrestrial plants is certainly the time it might take. This depends upon the plants, and I have no idea about terrestrial plants' rate of nitrate absorption. With aquatic plants, we know from scientific studies that faster growing plants like floating species can take up ammonia/ammonium as fast as it can be produced, and within reason it is impossible to add so many fish in the tank that this fails. "Ammonia sink" is indeed a good term for substantial floating plants. I would assume that faster growing terrestrial plants also have more rapid uptake of nitrate, but I have no direct knowledge on this.
As for nitrate "shock," I'm not sure that is correct. I went into this topic in detail with Neale Monks and the late Bob Fenner, and they unequivocally agreed with me when I said that moving fish from water with nitrate into water with no nitrates was a benefit the faster it was done. But in reverse, with water changes introducing high nitrate, I don't know, we weren't concerned with that. Someone on TFF insisted that the nitrates should be slowly lowered over weeks to avoid shocking the fish, and Neale said that was definitely wrong, the faster the better. You want to get fish out of water containing any poisonous substance as fast as possible, not dawdle over it. Given that nitrates slowly weaken fish, which then causes other problems because the fish is unable to adequately deal with them, I do not know what might be the effect of weekly "up and down" with nitrate. I certainly think the better and safer method is to do the removal of nitrate from the source water
before it goes into the aquarium, such as how
@AbbeysDad does it.