Is reality a dream? Simply, no.
Dreams are phenomenon occuring in sleep mode (you can also have hallucinations when you're awake). Dreams are the projection of recent memory of biological organisms operating at complete stillness at hyper-speed (or something along these lines; I study dreams and am an apt dreamer). Dreams are extracted, that is, whenever energy finds that it can withdraw a dream from your mind, there is enough interest to make it happen - a dream world is created.
On the other hand, our reality is part of the energy system in which energy of it can communicate with us directly. This is how we make the distinction but further, the Sun feeds the Earth, and Earth homes lots of life; this is a logical process - unlike a dream - you may sense the inner-working directly. Dreams are like conscious versus conscious versus logic, while reality is conscious versus logic versus conscious.
There is a middle-man in this reality, it differentiates reality from dream; if we cut out the middle-man, it is a dream. Who's to say if we cut the middle-man, a logical reality wouldn't manifest?
If you examine a dream closely it's like a blur or abstraction that easily fades. Like light dented space for a few seconds (that special effect you may know of). This is because the grounds for a dream are highly illogical, the reality is not there but it is perceived as if it were, that's a matter more of imagination.