I'd bet that it won't. Population growth is slowing here on Earth and likely to top out around 11 billion. Even so, people immigrating to Mars will be pretty limited by the transportation costs. Even with Musk's vast reduction, he's still talking about $500k for a ticket. Awesome! But...still very spendy and that will limit the folks able to go.
Then there is life on Mars. or rather the life people would live on Mars.
Mars is...a bit challenging to terraform as noted already just from the atmospheric POV. Then the soil itself is more than a little toxic: .5% of the martian soil is made of perchlorate salts. These are bad for people. Watney wouldn't have survived, at least as presented.
(still love the book and movie though)
Mars is pretty much a mega fund site. But not as bad as Venus.
RE: Will Humanity Turn Mars Into Trantor/Coruscant?