_Yes, but high-performance windows and exterior shading may save more_
While it’s theoretically impossible for anything to actually save energy, interior window shades can indeed keep summer heat out and winter heat in. The real questions then become: How well do they perform, and under what circumstances?
In the summer, shades keep out heat, but they also block light
Interior shades (and drapes, blinds, and the like) can reflect light energy back out that would otherwise be converted to heat energy inside the home. According to the authors of the best resource on the topic, Residential Windows (Carmody, Selkowitz, Arasteh, and Heschong), “drapes can reduce the solar heat gain coefficient of clear glass from 20 to 70 percent.” That’s a pretty big range. How well drapes exclude heat depends on the shade’s color (silver would be the best, black would be worst) and their proper use. They can’t block anything if they are not closed, and when they are closed, you of course can’t see anything out of the window, and you need to turn on a light inside (so, laws of thermodynamics notwithstanding, are they really saving energy?).
Exterior shading, on the other hand, performs better all around: It can deflect 100% of the direct solar gain, does not depend on occupant operation, and does not eliminate views. So, interior shades do work to reduce direct solar heat gain, they just do it rather poorly in the grand scheme of things.
In the winter, shades reduce radiant heat loss
You will see claims of up to R-8 by some manufacturers of interior shades in terms of reducing heat loss. Just as with insulation in a wall cavity, the insulating value of a window shade depends on a continuous air barrier being right next to it. How many of these interior thermal shades have an airtight seal around their perimeter? None that I have seen; instead, convective currents short-circuit the shades’ thermal performance. It is hard to say just exactly what their performance is, because there is no standardized third-party testing of window shades, as there is for windows. But be happy with a couple or so Rs, not R-8. And once again, you have to operate the shades to get their best performance. Leave them down or closed on a day that turns sunny, and you have a net loss of energy. Open or up at night—oops.
Interior shades can make rooms more comfortable. They have been shown to boost thermal comfort (raise the mean radiant temperature) by as much as 5°F. But just as with overall energy efficiency, improvements in thermal comfort with interior shades depend on how well the windows work to begin with. Improvements are highest and most noticeable with older, poorly performing windows. That bears repeating: Improvements are highest and most noticeable with older, poorly performing windows. Or put another way, good windows work better than shades.
So, interior shades can keep your house cooler in the summer (during the day) and warmer in the winter (at night). But for real energy savings and overall performance, go with high-performance windows and exterior shading, and relegate interior shading to handling privacy. After all, you put those holes in your walls for the views and the free light!