If by burden you mean performance, it’s possible, yes. However, you would need to load extremely large or complex CSS. In the context of theme components, plugins, or site customizations, it’s usually small pieces of CSS; it won’t have a noticeable impact no matter what you do.
In the worst case, you might slow the rendering process with inefficient selectors, the wrong use of animation, or font loading, but unless you have a huge page and do something very wrong, you will be fine. You can follow the best practices (there are many resources on the Internet).
Also, I think you will have a JS performance issue rather than CSS in most cases.