Following that line of reasoning, you could say that even the smallest particle/bit of energy has some level of consciousness.
Then you could also say that Earth (and any planet or star), is also conscious, and at a way higher level than we (humans) are.
Do you know of this concept has been incorporated into physics somehow? Are there any models in physics that consider panpsychism as fundamental? (i.e. That consider consciousness as a basic property of matter/energy, just like the 3 special dimensions or time)
What's the point of the word "conscious" if it's just a synonym of the word "complex"? If it doesn't add anything, it's not worth having the word.
However, this happens very frequently in humans, we have multiple different languages and even multiple synonyms for a lot of (most?) words in every one of those languages.
At the same time, would correlation of two things make one of them worthless to have/know/understand?
If you're saying they're synonymous, then it doesn't make sense to ask whether you can have one without the other.
So ask yourself, could you imagine something being complex but not conscious, or conscious but not complex? If so, then they're not synonymous and you have something interesting to talk about.
We us as humans on the other hand, want to compare our consciousness to the one of animals/plants/etc.
Trying to bridge the two things, you could say that everything has consciousness, but that there's a "level" of it, which to make it simple, you could attribute to (or be roughly correlated to) complexity/size.
In a way, it's exactly how gravity is defined.