No, they are not real.
To complicate the question a degree; Are thoughts we have forgotten real? Or rather, does a tree make a sound when it falls and nobody's around? What is real to us as conscious beings, is that which we experience. But we see through the lense of our mind, which is skewed by concepts of time, and self-agrandizing of itself for it's complexity. A forgotten thought is a lost one, and ceases to exists. In that, what is real, is that which outlives those who may observe. But, if this universe came from nothing, it will probably return to nothing. Therefore, we harvesters of thoughts are as unexisting as the world that surrounds us. The only way then for our universe to exist would be for a god who can witness it, like we might catch a glimpse of a single raindrop falling and disappearing into a puddle.