Yes and no.
Yes, Ico is about being alone, small, in a giant, cold and echoing castle, over giant cliffs with waves crashing in the distance at the bottom.
But I think Ico didn't had the impact of SotC has it came and went relatively unoticed by both audience and designers. Sure, it got a small following and a deserved cult classic status, but I don't feel that it has influenced games like SotC later did, or Call of Duty, GTA or Dark Souls did, even at its scale.
I also feel that SotC, while being vastly different than Ico, went back on a lot of its thematic and undertones and fleshed them out. While Ico is, in the end, a classic adventure exploration puzzle game, SotC was and still is, like nothing else : an open world, 16 bosses and that's it. No enemies, no camps, no secret, barely any collectibles. Its so focused, uncluterred and pure. It adds a lot to the experience imho, the feeling of loneliness, crushed under the infinite vastness of this empty, erie, almost desolate land. As much as the colossis themselves, I truly believe that emptying the entire map made it so much more iconic because it made us look and soak in at every ride we took, instead of most game where we are pushed to look for items, upgrades, secrets, and not look at the game anymore but at systems.