That would really depend on the specs of the monitor and the PC you'll be using it with. Old doesn't necessarily mean bad.
The most important aspects to consider are resolution and refresh rate. For example, if you're building a powerful PC that can run your favorite games on a 4k resolution at 144 FPS, that's a lot of wasted power (and money!) when it's all being displayed on a monitor that can't do better than 1920x1080 at 60Hz. That doesn't mean everything will suddenly look awful, but it does mean that your system is going to get bottlenecked by what your monitor can display and not live up to its potential. Of course, if you're not interested in playing games at a higher resolution or with more FPS and your build reflects that...