I don't think so. Let's be logical - consciousness, what is it good for? It protects the body, keeps itself alive. Then you can't have consciousness everywhere. It needs self replication, evolution and learning in order to exist. You need to have agent and environment in order to have consciousness, an agent with goals and needs, just any rock will not make a decent agent.
Also from a how the brain works point of view you have billions of neurons recognising things in parallel and the data seems to narrow down from that to awareness of a small number of things which you can logically reason about. I'd imagine a lot of the conscious experience comes from that - the neural net highlights as it were.
Like if you're in the woods your pattern recogniser bits may be going there's a leaf there, there's a twig there, there's a bear attacking, there's some moss on the tree etc. and then the bear bit will get highlighted so you can think 'ah pepper spray' or what have you. The highlights being what we experience as consciousness.
It implies you get human like consciousness from that kind of mechanism so yes for a mouse, no for a carrot.
It also differentiates stuff going on in your brain that you are aware of and respond to but are not consciously aware of to that which you are. Say you are being chased by the bear and run. The logistics of running - path dips 2cm, raise left leg 5cm... you will not be consciously aware of because the highlights and logical reasoning bit will be busy with 'shit -there's bear what next?' type issues.