Yes but the Jamestown colonist could be reasonably assured of finding food to eat, water to drink, air to breath, and resources to build shelter with everywhere. On mars you'd need factories just to produce each of those, factories to produce spare parts for those factories, and large scale mining to supply those factories.
Good luck shipping all of that to mars any time in the near future.
With our current level of technology we can probably get to mars, for maybe a trillion dollar mission we might even be able to stay a while. But to thrive would probably require a non trivial amount of the world's GDP working to supply such a colony for a very long time.
Just to put it in perspective it cost about a billion to put two 400 pound rovers on mars. Now think about how it would cost to put all the things that were required to build those rovers on mars and you might begin to approach the difficulty of building a thriving colony on mars. All the chip fabrication plants, all the foundries required to produce the metal, all the machines required to mine it, power plants, transport for the resources, you’d need things to make glass, plastic, 100s of different chemicals.
Baring some unimaginable break through (cheap, easy, and small fusion might do it) the best we can hope for in our life time is robot miners shipping resources back to earth and even that is probably unlikely when asteroids are so much easier to get to and back from.
Maybe we can vacation on mars in a few decades for a few billion, but anything more is science fiction at this point.