[eluser]Derek Allard[/eluser]
There isn't anything fundamental that I can think of... the inadequacies of that version of PHP will come from things like lack of support for certain functions that CodeIgniter relies on. If you wanted to try it, just ensure that your errors are turned on, and be sure to check every page you write. Its possible that you don't end up using any of the functions that require a higher version of PHP, but that said, its also possible that you'll invest large amounts of time getting 90% done, only to find that you can't build the last 10%.
Another thought... develop locally, and then release the website when PHP 5 becomes available.
Good luck! Please do report back here how it goes for you... you've got me curious