Yes—provided you have a valid, unused serial key. However, you face a practical problem: Adobe’s CS4 activation servers were shut down in 2019. Even with a legal key, the software cannot "phone home" to activate.
In the world of vector graphics, few names carry as much weight as Adobe Illustrator. For designers who came of age in the late 2000s, (released in October 2008) represents a golden era. It was the version that introduced multi-artboard support, a seamless Blob Brush tool, and a smoother gradient experience.
This is the most common result. These are pirated copies where the software has been modified to bypass activation. While technically "free," they come with catastrophic risks: