Can the demon be seen as the author and Tamara the reader?

That's certainly one way of interpreting the poem. The demon wants to seduce Tamara so that he can finally put an end to his days of lonely wandering. For his part, Lermontov hopes to achieve some measure of freedom through the act of writing.
Like the fallen angel, Lermontov was exiled. This was a common punishment in Tsarist Russia, where certain classes of criminal would be banished to some far-flung corner of the Empire. After being caught writing seditious poetry Lermontov was sent to the Caucasus, a remote, mountainous area in what is modern-day Georgia.
Although Lermontov made himself at home in this part of the world, and found the atmosphere much more conducive to writing, one senses from "The Demon" that, deep down, he yearned to be accepted once more into the bosom of St. Petersburg high society. As with the demon, Lermontov is a fallen angel who, despite his bad reputation, simply wants to go home.