Can i have a state in OS X where there is no default browser
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."