I would say you could certainly grow the plant (I've seen plenty of potted coconut palms growing in less than ideal conditions) but getting it to produce would be another story. I've found this generally to be the case with so many tropical fruiting plants: that growing them may not present much trouble, but getting them to flower, cross-pollinate, and bear fruit that is tasty and worth the trouble, is something different entirely.

Can you provide the right environmental conditions not only for the plant to thrive, but for the whole flowering, pollination, fruiting process to happen, which I assume takes several years in this species? And do you have the space and the patience to be able to wait many years for this thing to produce a coconut as your reward?

So in short, though there are many aspects to this that might not be feasible for you, it could still be an interesting experiment.