Simple answer- no.
But this does NOT mean the same thing as "habitat-living", which is possible for Mars!
Let's take a look: "Terraforming" means to take a planet (Mars) to be the same as Earth. Running liquid water, growing trees, wildlife, atmosphere- the whole caboodle!
It's not that easy. In fact, for Mars, it would be quite impossible. For Mars to be just like Earth, there's a few key elements missing from the equation: Atmosphere, magnetic field, and water. And there's one MAJOR THING Mars does not have compared to Earth- a rapidly-moving inner core.
That's right! Our iron core provides our magnetic field, which in turn helps sustain our atmosphere, which regulates our temperature and climate! Mars does have a core, but something in its dynamic past has since slowed it- wiping away its magnetic field and ultimately losing the atmosphere. Without a core system, even an induced magnetic field by astronauts would only be temporary.
And without a magnetic field and an atmosphere- you get LOTS of radiation! Almost to the point of having nearly 10 X-ray scans of your body PER DAY! And with that amount of radiation, the water is not going to remain a liquid on the surface- it's too cold and irradiated at the same time.
Terraforming is not the way to go for Mars, but building dome-like structures for habitats would be! Complete synthesized micro-environments. This could be our future for the Red Planet.
Thank you for reading and next week- a look at bubbles on Titan!