Not exactly. The wood Stradivari would have used to build the violin would have been aged for years, stacked with other blanks in a stable and dry environment with slats between each piece to allow air flow over all surfaces. The luthier builds the instrument "in the white" as both the spruce used for the top and the figured maple used for sides, back, and neck are very pale woods. When completed the white instrument would be exposed to the sun for a period of time, determined by the maker. The ultraviolet rays would turn the white wood a lovely honey amber gold, which color would provide undertones for the varnish.

I suspect that the violin is famously red because of the many years "out of circulation" and hidden in the dark. Instruments that are regularly played are worn by the player in predictable and often beautiful patterns. A diamond shaped wear pattern usually develops on the back from contact with the player's shoulder and chest, other high touch areas see varnish loss and in these cases some of that gold undertone shines through. The corners of the "C bouts start out squarish and angular but wear down over time in a classic round wear pattern, and often the varnish will develop a subtle "crackle" pattern.

Master luthiers today have learned to copy all these features of a century old violin, not willing to wait I suppose for a couple of centuries to let the users transform their work. The Red Strad, on the other hand is a better record of Strad's original intent. Sorry to ramble on so long, thanks for introducing me to this instrument and its history!