One customer running a single WordPress was using a 4x vCPUs instance on Amazon AWS®. But the CPU and load usage were so high, with no apparent reasons (the number of visitors was reasonable). Međutim: each 404 triggered a huge CPU and bandwidth consumption! A test was conducted and the 404 was replaced by a flat and tiny 324 bytes HTML file. The result: the instance size could be divided by two, so halving all expenses (including the bandwidth).
When using a custom 404-page: one should not forget that even a simple dead link to an image will trigger an expensive and huge HTML code being returned to the browser, resulting in sluggish speeds for the visitors as well!
In other words: do not do it, even if it looks pretty to the eyes.