No, I don't think it is wise to see emotions and intelligence as algorithms. It certainly isn't the traditional way to think about the world of human experience.
One reason to think of algorithims is that one can do things with them. Crucially this aspect is missing from intelligence seen as algorithmic.
One can certainly simulate certain kinds of thinking with algorithms but this does not show that they are the same thing. What one is doing is modelling. Physics, for example models the physical world - but one should not then make the mistake that the physical world is physics.
The Turing test takes a functionalist view of intelligence. Quite crucially Turing ignores the fact of inner life. I'd argue that thinking is intrinsically tied up with inner life. To ignore it doesn't mean that its not there, or that its not important, but renders the question more tractable.