Can i have a state in OS X where there is no default browser I'd like OS X to default to whichever browser is open (i.e. have no default browser) so that links in other applications don't go off and open a second browser. 

Is this possible (without copy/paste). An example would be that I'm listening to music in google music in chrome and i click a link in my Evernote and/or Wunderlist app and Safari is called to open; okay most times but not this particular time.
A number of apps will let you do approximately this, but as far as I'm aware only Choosy ($10) has the flexibility to decide which to use based on which browsers are open. (All of these apps are designed to let you pick a browser when you click a link, and some, Choosy included, also let you make rules based on the link URL or source app. If that's all you need, then you may find another option might serve you better.)

To make Choosy work in this way, simply install it, add your browsers to the "Browsers" tab in its settings, and then set the options in "Behaviour" how you want them. Based on what you said above, I expect you probably want to set the first option listed to "Use best running browser."