In the modern formulation and understanding of Maxwell's equations, yes, they do show that the speed of light is a constant. However, in the context of the time

In the modern formulation and understanding of Maxwell's equations, yes, they do show that the speed of light is a constant. However, in the context of the time they were written, it was not known whether or not that was a true fact of the universe or if that meant the equations were incorrect. In the historical context I'd classify it as a "clue" but not a proof. Proof really came from observations.