Depending on the content and nature of your website, I expect the likelihood of approval will vary from difficult to impossible.
I believe the policy is that you declare all your side projects, which get reviewed and approved by lawyers and you're then able to do what you like with them. 100% of projects I've heard people submitting have been approved.
Otherwise, the party line is that IBM hold the IP. I've never seen this happen in practice though.
Obviously don't work on side projects on company time. If you did you might have more than IP problems to worry about!
For example, I worked at a company last year. During the application process I asked about working on my side projects and about contributing to open source projects. After I signed my offer my recruiter let me know that she had received a response from the legal team. The consensus was that I'd be able to, but my code would have to be reviewed before it was released to make sure it didn't conflict with my work. I was content with that arrangement since the NDA was pretty restrictive.
When I started working I contacted the legal team to ask about the process, and I was told that my recruiter was incorrect, I would not be able to work on side projects or contribute to other open source projects.
In retrospect, I wished I'd asked engineers who worked there, not Human Resources. It probably wouldn't have changed whether or not I applied, but it was incredibly disappointing to be told I could do something, just to be told I couldn't actually do it once I started working there.