Are Synthesized & Fractured Items Counted as "Influenced" Items?

Question in title, but basically, I have checked the poe wiki (https://pathofexile.gamepedia.com/Influenced_item) and several other sources. But, is a synthesized or fractured item counted as an influence? Because from a t4 blue seed there are crafts that say:

"Remove a non-Influence modifier from an item and add a new Influence modifier"
"Remove a random Influence modifier from an item"
"Remove a random Influence modifier from an item and add a new Influence modifier"

Along with a few others, however, I do not want to just blindly test this and see. So, does using a synthesized or fractured item on any of these t4 blue seed crafting outcomes works? Has anyone tried this? Any help and/or answers on this would be greatly appreciated, thanks.

No. Influence is Shaper, Elder, or the 4 conquerors.