Can I use / view Ubuntu software online?

Go to http://www.ubuntu.com/tour/en/. You can directly show them the awesome Ubuntu software center from within your browser!!.

You should have flash plugin installed in Firefox. If you use chrome, you will be fine. To install flash use the below link:

flashplugin-installer

or using this command in terminal

 sudo apt-get install flashplugin-installer

Here is a screenshot running Ubuntu software center (full demo Ubuntu actually) inside a browser

enter image description here

You could definitely run an Ubuntu instance on some cloud provider and use VNC to "show" it. You can also use the web Gtk backend like this.