No, EV certificates are not possible with Let's Encrypt. Let's Encrypt is a fully automated service without any intervention of a human employee.
For EV certificates it's necessary to have things checked by an actual person. This is something that will not be happening with Let's Encrypt: the goal is to encrypt the whole web. This goal can also be realised with DV certificates. EV certs aren't necessary for this goal and Let's Encrypt can be free of charge because of the automation.