It's not possible for you to install third party plugins with OnDemand and you're limited to the plugins that Atlassian provide by default and unfortunately Theme Builder is not one of them. See http://confluence.atlassian.com/display/AOD/Atlassian+OnDemand+Plugin+Policy for details.
It may be possible for you to request plugins to be installed or asking if there are any plans to include Theme Builder with OnDemand by contacting email@example.com
Even without the Theme Builder plugin it should be posisble to make certain JIRA projects public through a public page in Confluence. If you had Confluence Space that was visible to anonymous users you could use the JIRA Issues macro (http://confluence.atlassian.com/display/DOC/JIRA+Issues+Macro) on a page in that space to display the issues from a JIRA project in a public Confluence page. IS that along the lines of what you wanted to do?
Hope that's of some help?
EDIT: See http://confluence.atlassian.com/display/AOD/Restricted+Functions+in+Atlassian+OnDemand for details of the general restrictions with OnDemand
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