Can I use TightVNC on a Linode?

You can do this, however in most cases it is not recommended due to the requirement of installing a Desktop Environment like Gnome, KDE, XFCE, etc… If you do decide to do so, I recommend using something lightweight, like XFCE, and avoiding resource-intensive DEs like Gnome and KDE entirely. The reason this is not recommended is that most of our plans do not include GPUs. We do have GPU plans available now, which you can find on our Pricing Page, but these plans are intended for GPU-intensive tasks, like machine learning, and are admittedly a very expensive way to go if all you need is to add a DE to an otherwise lightweight server.

That said, we have a guide on installing VNC on Ubuntu 16.04, but it does not appear to be using TightVNC. I also found this guide on installing TightVNC on various Linux distributions, which may be more helpful in your case.