Your question is inherently problematic because FTL travel redefines the role a single planet plays....
Out of practicality, not every place on earth can be "ecologically diverse"...people have to live somewhere, and therefore earth has both ecological havens and super urban metropolises...we protect the environment of certain "regions" because those regions are more beautiful/special/ecologically diverse...other regions that are not as "special" are not safeguarded as parks or reservations, and therefore are open to development...
Ideally, we would protect our rainforests and other areas of ecological diversity while developing "bland" areas of the planet for industry, commerce, and housing...but, that's only because we have one planet...
Imagine instead that we lived on all the planets/moons in the solar system...certain regions would be protected since they are seen as ecologically diverse (ex: earth)...other, more bland regions would be heavily industrialized (ex: mars)...in essence, this is precisely what we do now: specialize land...however, instead of specializing continents, states, or provinces, we would be specializing entire planets...
Asking to industrialize/populate/develop a planet while also preserving its ecology would be like asking to develop New York City while also protecting its environment...while you can reduce pollution, etc, you can't maintain ecological diversity in the same place you manufacture and live...
Obviously it is possible...after all, we do it with far inferior technology...however, I highly doubt we would treat the earth the same if we had multiple planets...if those planets were far worse than earth, then nearly all industry would be on those planets and earth would only be used for housing and recreation....if those planets were far better than earth, then most likely the entire ecology of earth would be destroyed and the better non terran environments protected...
The answer to your question is unequivocally yes if you consider the current state of earth "ecologically diverse"...however, for a nation with many planets I find it unlikely that a planet like earth would be as heavily industrialized as our own (at least relative to their other planets)....
