The thing about evolution is that it takes a long time. It also leaves traces. Any sentient/sapient life that is curious about its environment is almost certainly going to discover these traces.
From this website, in reference to an arsenic-based life form:
NASA is saying that this is "life as we do not know it". The reason is that all life on Earth is made of six components: Carbon, hydrogen, nitrogen, oxygen, phosphorus and sulfur. Every being, from the smallest amoeba to the largest whale, share the same life stream. Our DNA blocks are all the same.
Silicon-based life is unlikely to occur naturally on Earth, given what we currently know. There may be silicon-based life forms in as-yet unexplored regions of the world, such as in the mantle or at the bottom of the ocean, but I consider it fairly unlikely (but not impossible).
So, having silicon-based life evolve alongside Homo sapien, on Earth? I'm inclined to say no. (Also, if it did, it wouldn't resemble a computer.)
Edit, to address comment about AI-directed life forms:
If mankind were to develop an AI capable of or instructed to build silicon-based life, there would be an entire team of hardware and software engineers somewhere who knew the AI could/would develop life. Its progress would be monitored closely, since mankind is curious about everything.
Let's suppose there was an extraterrestrial species that constructed an AI and it, for some reason we don't care about, found its way to Earth. It could conceivably foster silicon-based life on Earth, from the original formation, through development, to the end product. However, such an advanced AI likely wouldn't allow for evolution. Instead, it would build the new life to fit a specific role, allowing no deviation because that would be inefficient.
But what if the AI didn't care about efficiency, or it had curiosity? It could program its silicon children to adapt to their surroundings. Now we've got a new problem: competition. These silicon bodies are going to be competing for resources with native Earth fauna or flora, which is going to upset the balance of life on Earth. Homo sapien may very well never evolve in the first place because the niche filled by a critical link in our evolution was instead filled by these silicon bodies.
Maybe we inhabit completely different areas of the world, though. What if the silicon life forms are extremophiles and live at the bottom of the ocean or in the mantle? Now we're back to the original point of my answer: silicon-based life forms might very well exist in places we haven't been to yet. If they were in the mantle, however, volcanos would be likely to spew them out at some point, and we would definitely notice that. Since silicon-based life likely doesn't work with Earth digestive systems, fish we pull from the deep ocean would still have specimens in their stomach (assuming the fish eat them in the first place). If these life forms are small, this is likely; fish will eat anything they can find in the deep ocean.