Parts of the cosmos for sure are and there's no need to look very far for it - for example the part that forms me writing this right now is, in fact, conscious.
If the cosmos is conscious in the way that we are and the speed of light proves to be a limit, then its thoughts would take thousands or millions of years to process. It may be compelled to leverage entities with cogitation components within light seconds of each other for fast thinking. The Thinking, Fast and Slow paradigm could be built into the shape of the universe.
If the slow thinkers seek to constrain the fast thinkers we may get away with a lot before they catch up.
If the speed of light is a hard limit, leveraging localized cognition would not be useful at all. The localized cognition would only be able to ponder things it observes or experiences, that is, it can't ponder whatever the conscious universe wants it to, so the universe has to create it where it needs it, and then it can't use this cognition anywhere else because again, the speed of light. It really gets us nowhere.
I think though probably this "consciousness" of the universe, if it exists, is apparent and localized, but not bound and distinct locally, if that makes sense.
> then its thoughts would take thousands or millions of years to process
This reminds me of "The Hitchhikers Guide to the Galaxy", where pan-dimensional beings waited 7.5 million years for their first super computer to tell them "42". Then they constructed another super computer, Earth, to find the question.
>If the cosmos is conscious in the way that we are and the speed of light proves to be a limit, then its thoughts would take thousands or millions of years to process.
No. Entanglement does not allow information to travel faster than light.
You can instantly know the state of another particle by measuring it's twin, but you can't do anything useful with that info until you share the results of your measurements (at the speed of light).