Not in the official list, but not locked out, eiither
Opera and Chrome aren't in the list of officially supported browsers, but unless a lack of support can be shown to arrise because a failure of the web app to support Web standards, wherein lies the problem? This is why you build to standards, in the first place: in order to stop having to explicitly name the browsers you support. It should be implicit. A browser's quirks (should they exist) could change at any moment, with a software update from its maker, so there is no point supporting them if you can avoid doing so, since they should not have been there in the first place. Build to standards, and you can assume that what you build, today, will work in browsers yet unwritten - at least until the Web standard you were building to, itself, becomes defunct.
A lack of support for Internet Explorer 6 is much less surprising, in this sense, (regardless of the fact that it was, once, a Microsoft product) since IE 6's support for the Web is by far the worst, among commonly used browsers. Would we be surprised if Microsoft said it wasn't going to support Netscape Navigator 4.0 - after all, that's a Web browser, too? Of course not. Niether browser was built for the Web, but for some version of the 'Web' that both companies tried to foist upon us, at the time. That time has passed, a new time has come, when some triage should be applied.
Whether Opera and Chrome manage with heavy use of AJAX-driven in-page events, and so on, may be another question that influences their ability to work with an online version of Office. However, given that it will be unlikely that Microsoft would be able to market an online Office suite that did not meet certain levels of Web Accessibility (given the very nature of the product), then the scope for including deliberate proprietary lock-out is potentially limited. It is legal (although probably follisome) to deliberately not support users of a given Web browser, but it is against the law to try and market some types of software that don't support Web Accessibility. I'd guess Office Online would almost certainly fit into this category - so even any unintentional effects that caused degradation in otherwise compliant Web browsers would probably be best avoided, since they could have knock on implications for Web Accessibilty (and hence the overall legality of the product). This could prove far more costly than any phryic satisfaction to be had from driving away a few Opera users.