Maybe, but there's a good amount of things connecting it to the apostles that would lead to confusion for it to be something outside of them. Like the fact that it needs a stronger connection via evolution, or that line at the start of the Cole fight "L-LIfe. The birth. A product. What came before."
The Eye being Evolution is by far the most likely option, but I think the possibility of it being other thing is also on the table, even if the "evidence"(add more quotes) is less than the one pointing it to actually be the Arbiter. The comment of the Silat for one, but also the lines you mention, Life, Birth, what came before, some of the concepts that the Eye uses to refer to itself seem more tied to Life/Origin as a whole rather than just Evolution, like when the Eye tell MC that he is connected to "Every Branch", and he only chose MC because he was the best option at the time, but other, better vessel may have been born since then, but there aren't any other Spawn of Body/Memory around as far we know, which make me think, the Eye is connected to every branch, as in the Twelve Traits, not just 3/4
Then there is the Eye's words back on Battle of Diamonds, there it says that Hex was born from him(when talking about the parallel dimension), and regard all Monsters and Spawns present on the battle as their tainted lineage, born from him but that he can't abide it, Hex is Ether(and time probably)and most Monsters/Spawn have a bunch of mixed traits, still, the Eye regard them as offshoots of theirs, all this to say, I think the Eye, rather than Evolution, might be something different, behind the line of Monsters, like, Eye>Arbiters>Apostles perhaps. Also the Chaos memory in which is implied how the 3 Arbiters that did prepared lost in the end, mention "We three and one another", when talking about their eventual revenge, that might have been the eye, but if it is an Arbiter itself, it would be weird to just simply not include it with the three, instead of make that distinction.