To a point, yes.
Some parts of the structure are going to be tough to change. The foundation, framing, wiring and plumbing all are components integral to the house. Although an unlimited renovation budget opens all kinds of doors, altering these parts of the house can be very expensive and beyond the means of many homeowners.
That said, there are many upgrades and changes that will make a house more energy efficient, healthier and more durable. Upgrading windows and heating and cooling equipment, putting more insulation into the attic, sealing air leaks, installing ventilation equipment, and switching to low-VOC paints and finishes all are examples of positive steps. (VOC is shorthand for volatile organic compounds, which include environmentally harmful solvents that evaporate into the atmosphere after paints or other finishes are applied.)
Keeping sustainable building practices in mind during routine maintenance and repairs can help. Let’s say you need new siding. Wrapping the house with an inch or two of rigid foam insulation before the new siding goes on can mean substantial energy savings. If you need new windows, why not choose high performance versions designed for your climate?
Once again, it boils down to applying the principles of green building to the decisions we make. Books and magazines that routinely deal with this topic are a good start.