Probably not to the degree you are referring to. Microscopic life is "intelligent" in the way all life is- it reacts to things, it fends for itself, it will run from danger.

Is it self aware? Most likely not. Complex thought in humans comes from the frontal lobe of the brain which took a very long time to evolve. It also came in part from our omnivorous diet and more dense complex foods that we eat to maintain the energy to have those thoughts.

I do not know if the size of our brain is really necessary, but it would VERY LIKELY need to be bigger than microscopic. The more cells there are, the more complex the organism is likely to get. You would probably need something multicellular and with enough cells to be physically capable to form a memory so they can have a sense of "self".

Memory is a bit like "Bop it!". Remember that game? When you have an experience, you have a combination of sensations. When you REMEMBER an experience, your brain is firing off the same combination of senses- as similar as possible with the time that has passed. Thats why a memory feels like you are "there again". But there are so many combinations of cells to fire at once in a small organism. What if all you have is "bop it, twist it, pull it" and thats it? Lets say each "bop" "twist" and "pull" trigger is a neuron. Theres only so many combinations you can make with that...theres only so much that could be recalled. What if I added a dozen more buttons? 2 dozen? a hundred? Now we are talking more possibilities. More COMPLEX. The more combinations there are, the more in depth can be recalled. Thats....putting it pretty simply....but this is just to give you an idea of why bigger brains tend to be smarter brains.

Something so little that it feeds on simple foods would not likely have the proper inflow of matter to sustain such a complex network of cells.