Of course he dreams. Even when he was only in his eighth incarnation.
In recent years during Doctor Who panels at conventions, it's been rather fashionable to have previous Doctors read some dialogue from modern Doctor Who episodes to hear how their Doctor would sound in the same scene. Past efforts have included Colin Baker reading "The Rings of Akhaten" speech and Sylvester McCoy reading from "The Pandorica Opens."
Well, one of the latest recreations took place this past weekend at Comicpalooza 2014 in Houston, Texas, this time with the Eighth Doctor, Paul McGann. During a Q&A panel moderated by Jesse Jackson, one of my oldest friends and fellow former member of the comics APA TitanTalk, McGann was asked by a woman named Molly Martin to either sing something or read the final monologue from the Doctor Who 50th anniversary special, "The Day of the Doctor."
McGann thankfully opts for the latter, putting an Eighth Doctor spin on the special's final scene where the Eleventh Doctor gives a voiceover monologue about what he dreams ahd where he's going, then leaves the TARDIS to join his previous eleven incarnations (including John Hurt's War Doctor).
Despite joking about setting himself up for a fall, McGann gives a lovely delivery that starts around the 1:09 mark. Here's the video found on YouTube, thanks to user Adam Perez...