The short answer is no. The long answer is that the effects of applying paint with and without priming are different. Both methods can be used to create unique artwork. While leaving the cardboard unprimed will end with a less durable piece, the tone created by soaking more of the color of each paint and the effect of dense layering can be used in creative ways.
Primed cardboard leads to a more traditional surface that can be used for a wide variety of artworks with consistency that lasts.