Yes, in my opinion Yahoo can stay afloat after the Alibaba IPO. Yahoo is a company that has been around for a long time, and has continued to survive even in the face of Google and Microsoft. I do not believe that something like this will be the death of Yahoo, it may just make them take a different approach going forward.
Yahoo is such a well known name in the business and is known by millions of people across the world. It also has several contracts linked up to email providers & mobile phone contractors that seems to be a profitable relationship for yahoo & it's partner companies such as sky & btinternet.
I do not think yahoo has anything to worry about. They have been around for a while and will continue to flourish. A lot of people use yahoo for email, news and everyday life. I personally use yahoo and I'm very satisfied with the service. As far as staying afloat after Alibaba IPO, I say of course it will stay "afloat".
No, I really don't believe that yahoo can stay afloat because even before the Alibaba IPO, Google completely has taken over 95% of the search sites including bing, yahoo. I think that all of those sites had almost no hope left. Google is by far the best and most accurate browser. Therefore, yahoo went down a long time ago.