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). למרות זאת: 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!
במילים אחרות,: do not do it, even if it looks pretty to the eyes.