According to a senior member of the Google team, a site with no incoming links once submitted to Google will be indexed and rated according to its relevence to each particular search query subject to the normal Google PR weighting.

Without incoming links, this would be an "Orpaned Site" and the only PR rating for each individual page would be generated by links internaly from other pages within the site. In other words an extremely low PR and a handicapped performance as a result.

Incoming links are required to achieve any sort of useful positioning return in Google because of the PR weighting factor unless the site is competing in a specialised field with little serious competition.