Is pulse audio absolutely necessary for skype to work?
No.
I tried for hours to get the mic to work in skype. I know the mic is working because I can get it to generate feedback with my speakers 
But it just won't work with skype (and possibly with some other stuff like audacity).
Feedback is one thing .... but can you hear your voice from the speakers?
At one time I had pulse audio installed and enabled, and it seemed to cause other problems (I forget the details, but I think some media players produced no sound), so I removed every trace of it I could find and made sure alsa was fully installed, etc. The problems I'd been having (mostly) went away, and I think they finally disappeared completely by removing phonon-vlc.
PulseAudio does not affect what media players themselves produce ... it helps you, via GUI, to choose source and sink.
PA uses Alsa.
Looking around, it seemed that advice here was to stay away from pulse audio unless needed to support certain hardware (?), and it seemed problematic for other reasons, so I ditched it.
PA has little or nothing to do with hardware support.
So, do I need to reinstall it?
PA is an audio management layer.
It helps greatly when managing audio to or from multiple devices.
If you have only one audio device/card then it is unlikely that you will get much benefit from it.
On the other hand if you have such things as multiple sound cards; USB speakers; wireless headset; bluetooth earpiece etc etc etc or if you wish to send or receive sound over the LAN, then it is of great benefit.
It also has easy set up of loopback mixer for mixing sound streams and recording them, and has an impressive equalizer.
