Can I access a server running on the Hotspot computer?

Yes! Connectify Hotspot allows you to access a server running on the device hosting the hotspot. If you are having difficulties make sure your firewall isn't blocking the port through which your server is running.
Another thing to note is Connectify Hotspot's Firewall options, which you can see here. In order to access the host device make sure that you have Local Network Access enabled.