With today’s technology not really; we can just barely reach it. With future technology, certainly.
With a large enough investment in time perhaps, but I doubt it would be worth it. Given the sheer bulk of Mars, it would take far less time and effort to set up some huge orbital system of mirrors to redirect sunlight than it would be to spin up a whole planet.
The simple answer is no, it is not possible with conventional technology or a simple extrapolation thereof.
The more extensive answer is that while we could not terraform Mars to simulate a terrestrial environment with existing technology, we can conceive of the technology that would be required to transform Mars, e.g. covering the surface with photo-absorptive algae to melt the polar caps, smashing the surface with water-bearing comets, et cetera.
However, by the time we would have the technology to realize this, we would have the existing space infrastructure to build large solar orbiting structures such as “Culture”-type oribtals, O’Neill colonies, or Easter Eggs (fiber-reinforced ice-matrix spun habitats) that could support a similar population of people for a fraction of the effort for terraforming a world, and which have the advantage of being mobile and readily protected against any natural threat or disaster short of the Sun going nova. There is very little reason for terraforming worlds at that point when we would be able to replicated terrestrial environments in a more controlled and readily-regulated manner.
One of the problems with terraforming you can see right here on Earth - the climate catastrophe we are having right now. Basically, laymen may think we understand how the systems of a planet work together; but scientists have become more humbled and learned of the chaos theory, and generally no longer believe it possible to influence such a complex system like a planet. Sure they can point to x affecting y, but that doesn’t mean they feel confident to doing 3.5 amount of x to produce y because of the problem of things running away and hitherho unknown relations and effects between x, y and r, s, t influencing u, v and so on.
Esp. given how little we know about Mars, compared to Earth.
Flying there and setting up little domes where people can live, and having artifical climate inside, - that’s possible and plausible, and sensible.
No, they believe we can influence the planet; just look at the various proposals for using some kind of climate engineering to combat the greenhouse effect. They just don’t have the level of confidence they would like in the results, and even less of correcting any mistakes. Except in a desperate situation, “we think it’ll probably work” isn’t good enough when we have only one habitable planet. And it’s not just the fact that the system is chaotic (in fact, the system being chaotic makes it potentially easier to manipulate), it’s that we still have a shaky knowledge of how it works at all.
There are many big projects we could do, a transatlantic tunnel, reforming Mars, flying to the stars. But who wants to pony up billions of dollars now for some benefit in 150 years? Perhaps with cold fusion and basketful of Star Trek technology, terraforming could be done, but only when the cost and speed of doing so is fairly trivial.
IIRC Mars, in terms of size, weight and surface temperature, is right on the cusp of being able to hold oxygen in it’s atmosphere (though maybe I’m thinking of CO[sub]2[/sub], in which case oxygen, which is lighter, would evaporate even quicker) . Which means it can hold oxygen for a while, but eventually it will evaporate. If you found a way to warm Mars up you’d find the oxygen would find this evaporation would speed up.
I think the answer is that Mars is possibly terraformable, but on some, not massively vast, timescale, simple physics will return it pretty much to it’s current state.
IMHO, we’ll have invented Von Neumann robots (machines that can build copies of themselves) long before any terraforming or serious colonizing of Mars can take place given how long either of the latter two are likely to take. At that point, the costs drop to whatever it takes to design a single machine and get it to Mars; given time a single such machine and its progeny could rework the whole surface of the planet just as life has reworked the surface of Earth.