Often people ask me whether shared hosting will work with Drupal, and I tell them what I have read. That is you need to be careful and select good hosting. The purpose of this Drupal 7 site is to test ICDSoft hosting and that is all it will ever do. Don't look for a fully developed site here ever.
I'm a reseller for ICDSoft hosting and have about 8 clients that use them, but none of these accounts are Drupal installs. I posed the question to their support folks and they said it works great and they have thousands of Drupal installs using their hosting. I wanted to try it myself so I talked their management into giving me a free account for this testing purpose. I get an affiliate commission if you follow my links and make a purchase with them.
What we are using is their $6.00 per month plan and the USA datacenter. I will only be testing this on ICDSoft since I have a long history of happy service with them, and find their tech support way better than any other that I have used. It is sad for me that they don't have a VPS package. If they did I would be there.
Here are the Drupal hosting requirements which is a must read before you pick hosting. Also read Webhosting issues from the Drupal site that starts with this sentence;
A lot of new Drupal users run into issues getting Drupal to work properly on their webhosting.
This install of Drupal 7 went without a problem. I just uploaded the compressed files to the server space and unpacked them. I used a Drupal Profile called GrandFoo Install Profile which I developed for testing another module. I used it because it has a lot of other modules with it and wanted to see if any of that extra weight would create a problem.
This install was originally done on 07/11/2011 with Drupal 7.2, and has since been updated without problems to the current version which is 7.7.