Not at all. There are no courses necessary before studying the CCNA. It is designed to take you from a position of no networking knowledge, to knowing a great deal about how networks operate, and how to configure the basics on Cisco routers and switches.
Many people find it useful to have both certifications, as this gives you a broader knowledge from both the network and from the systems side, but neither one is required before taking the other.
In fact, you might want to focus on one. Most managers even today expect a person to be a ‘specialist’ and if they see both certifications, they start wondering….
You should get both, because as pointed above it gives you a broader view. But when applying for jobs, stress one over the other rather than making them appear equal.