Yes. There are no show stoppers. The main problem is how to get there fast, cheap and safe. That, in turn is an energy source problem. We need to go beyond chemical rockets (which were invented in China nearly a millennium ago).
Mars is a tempting prize. Mars colonization will double the extent of land humanity live on. Indeed the Red Planet is endowed with nearly as much surface area as all of Earth’s land surface combined (145 million square kilometers for Mars, 149 x 10^6 sqkm for Earth’s continents).
Mars’ rotation axis, over the eons, wobbles impressively. Right now, it’s half way (same inclination as Earth’s). But when the axis is fully inclined, my bet is that the poles melt. Then Mars has got to become much warmer, and wetter: the atmosphere would be full of H2O, water, a powerful greenhouse gas. Maybe life blossoms. Hence Mars is even more interesting than it presently looks (one could imagine life adapted to these super-summers).
Could we conquer the seas instead? Sure, we have to. However, it’s more difficult. How could it be more difficult to conquer the ocean? The average terrestrial ocean is 3,688 meters deep. This means that we have to handle, to live there, a pressure difference of 370 atmospheres. On Mars, as it is, the pressure is 1% of one atmosphere; that is just one atmosphere difference. A light spacesuit can handle Mars. But just going down 20 meters in Earth’s sea doubles the pressure problem we have on Mars.
Radiation on Mars, and getting there, is a problem: a year stay, with the trip, would augment the probability of getting cancer by 5%. NASA, and radiation workers’ limit is 3%. The average smoker doubles his cancer habit from his gaseous drug habit. Thus, by only sending smokers to Mars, and thus preventing them to smoke (the fuel debris smokers smoke clog air filters), one would vastly diminish their probability of them getting cancer.
The problem with Mars is how to get there. Getting in Low Earth Orbit (LEO) is already (very) difficult, expensive, chancy, and will stay so, barring huge advances in material science. We need better engines, better airframes, and, or, a space elevator. Work is going on, in a number of ways, from perfecting launching rockets from planes, to airbreathing reaction engines, to the simple Ariane 6 solution of switching to solid rockets (French and American ballistic missiles are 100% dependable, as they sit in submarines stuffed with thermonuclear bombs).
Some hope that space tourism (one day in LEO for $50,000, say) will provide incentives for cheaper ways to leave Earth. Maybe, but university departments working on materials built atom by atom, better get lots of money (such materials, for example nanomaterials such as graphene, can be hundreds of times stronger than steel; we need to make them work on a large scale).
Given energy, rocket fuel can be made on Mars in a number of ways. Thus, plenty of energy, plenty of fuel. There is plenty of water on Mars (the Curiosity rover found between 2% and 3% in the soil). At least, at the poles (and perhaps all over). Some universities are already bioengineering mosses and other plants to survive on Mars.
With existing technology, and materials, we (or, rather, robots) could build a Space Elevator on Mars. So Mars could turn into a very convenient outpost, while terraforming proceeds.
To get to Mars fast, and to have the plenty of energy we need there to fuel robots, which, in turn, will be able to dig in the ground and make vast caverns and the like (etc.), we need a concentrated energy source.
There should be a crash program on these (while pursuing steadily ITER).
Mars had life and an ocean, for probably at least a billion years. Not having a core nuclear reactor, hence a protecting magnetic field and plate tectonic, Mars lost liquid water, warmth and most of its atmosphere (Venus has the same problem, although Earth sized). Mars is waiting the human touch to smile with exuberant life again. Colonization can expand diversity as it most often does (will cynics add perfidiously). Besides, a Mars polis would be an insurance policy.
The only way to not being able to colonize Mars? If civilization collapses first, it won’t happen. Unlikely? This is exactly where abusing fossil fuels is leading us.