I would not expect it to. Typically in a shared hosting environment you only have access to a limited number of ports. Typically only port 80 is a available. For example if multiple users attempt to run a service that binds to a specific port, then only one can grab the port, everyone else is out of luck.
So you want some variation of a VPS (virtual private server) where your running under a virtual machine, but it looks like its your own private machine. You get a complete set of ports to bind services to.
I've been using slicehost for a few years and been happy with them, you could look at amazon web services, there are many choices.