How pervasive is Flash?

Hi everyone. I’m just about to begin developing two websites, and I had a question for you web design experts:

Is Flash pervasive enough to be used without a splash/intro page for a major website? For instance, I’m going to be developing a site for a large nanoscience research institute (see this thread), who needs their site to be basically an advertisement for the National Science Foundation so they can get funding. I’d like to incorporate an embedded flash element in their main index, but I’m afraid that this could present compatibility/accessibility issues.

Obviously there are many large corporate websites that use Flash to great effect, without worrying about who won’t have it. But are there any real statistics on this? I’d like to have some data to present to my client about this issue (they’re all scientists, after all).

Thanks in advance if anyone knows something about this!