Even Westwood officially said that there is no link between the Red Alert and Tiberian timelines. Originally, there was going to be, but they killed that idea rather quickly.
So no. Red Alert is not the prequel to Command and Conquer.
Besides, the thing most people throw up is that a Soviet victory could lead to the Tiberian timeline, completely ignoring that if the Soviets won, there were entirely too many things that would completely prevent the formation of GDI it's not even funny. You would be forced to build it from an Allied victory, which already leads to Red Alert 2. No matter how you slice it, it just doesn't work.