Original by Philip Gibbs, 1997.
Yes. π is a mathematical constant usually defined as the ratio of the circumference of a circle to its diameter in euclidean geometry. It can also be defined in other ways; for example, by using an infinite series:
π/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - . . .
In general relativity, space and spacetime are non-euclidean geometries. The ratio of the circumference to diameter of a circle in non-euclidean geometry can be more or less than π. For the types of non-euclidean geometry used in physics, the ratio is very nearly π over small distances, and so we do not notice the difference in ordinary measurements. This does not mean that π changes, because our definition of π specified a euclidean geometry, not physical geometry. No new theory or experiment in physics can change the value of mathematically defined constants.