I would say yes, it is important to understand design, but don't panic and don't let it put you off. There is a bit of a myth around that design can't be learned and that you either have it or you don't, but I don't agree with that. Design is a process that can be learned.
There are a multitude of courses that you can do, both on and offline, and you will already have a head start in that you've already been exposed to design in your existing job.
More important than making things look pretty, UXers need an understanding of the design process, and have the ability to clearly communicate that process.