No, because that isn't how moves beating each other work (no such thing as "priority values"). They just gave the Weave hitboxes the clank property, the same as most projectiles; they just happen to not be multihit projectiles, so nothing happens once the one hitbox clanks. They didn't literally go "this acts as an item". It's the same as using nair through e.g. Aura Sphere, Pikmin smashes, Link arrows, Luma upsmash (but not Rosa's), Bowser Jr's cannonball, ROB gyro, Villager slingshots, among other moves.
The reason you can use nair through Witch Time and still clank with the Weave is because only one hitbox of nair is canceled by Witch Time, while the second one is still active and can clank. After that there are no more hitboxes, so you can't for example clank with a Weave and then also hit Bayo, but if you don't clank the second hitbox you can hit Bayo. Also, this whole thing assumes that Witch Time activated from nair's strong hit; if it's the weak hit, that's the only active hitbox, which is canceled by Witch Time and you can then get hit by a Weave.
I haven't checked, but this is also very likely the reason why you can nair though Corrin's fsmash. Same deal.