I don't know what you mean by "current hosting issues", but if any, you should report to your provider.
About the question, I understand what is your problem and I had the same question too in the past. In my case I installed Wordpress inside a folder called /news, as it was the purpose of the blog, to act as the news platform of the main site.
In terms of Search Engine indexing I saw no difference for my other Wordpress blogs, just make sure to have it right and have Webmaster tools correctly configured. Everything should be fine.
About the redirect, make sure you do it with your .htaccess in order to give Search Engines the information that this is a 301 permanent redirect:
Redirect 301 / http://www.example.com/wordpress
Keep in mind that this way every request on the main link will be redirected to the Wordpress installation.
Other methods are available, I found this good script that can help you.
@closenoc - I confess I didn't understand your comment, why should he use a non-predictable directory name for security reasons? the goal here is to make the site available for SEO reasons.