Theoretically it can, but practically it depends on hosting provider to have such infrastructure in place.
Node comparing to classic web platforms is self-sustainable platform. In case with PHP (for example), it runs on with of apache or nginx (or any other), and PHP it self is just script language with some libraries that does not do much apart of logic implementation, and requires web server solution. Web server creates socket to listen specific ports for traffic, will do its own magic and will execute PHP to process requests.
In meantime node.js creates own socket, and binds it to own port. That gives it much more low-level access, so it is web server it self. You can’t bind to one port two applications, so it already unsharable.
There are services (web servers) that allow you to create proxy to route traffic to your node.js process but that is not as efficient in some cases, and shared hosting does not provide such functionality.
As node.js is still fairly young as well as is well, different, it still did not hit majority of shared hosting services. There are some available services online to host your node.js applications in a ‘shared’ manner.
Additionally you can rent EC2 Micro instance on AWS for free (Free Tier) for one year, which gives you plenty possibilities and time to try and test different stuff. You’ll get semi-dedicated system, where you can do pretty much anything (install software, modify OS configurations, and much more), where shared hosting would not allow you to do so.