Yes, the magnitude of something's 4-velocity vector is always c^2 (set it to 1 in your unit system) by definition. It's not as simple as a R^n vector because you have a time coordinate of opposite sign and you switch coordinate systems by Lorentz transformation, but it's the right intuition. (It's complicated further in the presence of gravity, where you need an enriched differential geometry notion of a velocity vector since the spacetime is curved.)